{"id":1238,"date":"2024-09-10T18:31:16","date_gmt":"2024-09-10T18:31:16","guid":{"rendered":"https:\/\/gbelentzas.sites.sch.gr\/?p=1238"},"modified":"2024-09-14T05:34:46","modified_gmt":"2024-09-14T05:34:46","slug":"2-1-%ce%bf%ce%b9-%cf%80%cf%81%ce%ac%ce%be%ce%b5%ce%b9%cf%82-%ce%ba%ce%b1%ce%b9-%ce%bf%ce%b9-%ce%b9%ce%b4%ce%b9%cf%8c%cf%84%ce%b7%cf%84%ce%ad%cf%82-%cf%84%ce%bf%cf%85%cf%82-%ce%b1%ce%be%ce%b9%ce%bf","status":"publish","type":"post","link":"https:\/\/gbelentzas.sites.sch.gr\/?p=1238","title":{"rendered":"2.1 \u039f\u03b9 \u03c0\u03c1\u03ac\u03be\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b9 \u03bf\u03b9 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03ad\u03c2 \u03c4\u03bf\u03c5\u03c2 – \u0391\u03be\u03b9\u03bf\u03c3\u03b7\u03bc\u03b5\u03af\u03c9\u03c4\u03b5\u03c2 \u03a4\u03b1\u03c5\u03c4\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 (\u0398\u03b5\u03c9\u03c1\u03af\u03b1)"},"content":{"rendered":"
\n

<\/i> \u03a3\u03b7\u03bc\u03b5\u03b9\u03ce\u03c3\u03b5\u03b9\u03c2 \u0398\u03b5\u03c9\u03c1\u03af\u03b1\u03c2<\/em><\/span><\/h4>\n<\/div>\n

 <\/p>\n

\u03a0\u03bf\u03b9\u03b5\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03c0\u03b9\u03bf \u03b1\u03be\u03b9\u03bf\u03c3\u03b7\u03bc\u03b5\u03af\u03c9\u03c4\u03b5\u03c2 \u03c4\u03b1\u03c5\u03c4\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2;<\/strong><\/em><\/span><\/p>\n

\u039a\u03ac\u03b8\u03b5 \u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c0\u03bf\u03c5 \u03c0\u03b5\u03c1\u03b9\u03ad\u03c7\u03b5\u03b9 \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ad\u03c2 \u03ba\u03b1\u03b9 \u03b5\u03c0\u03b1\u03bb\u03b7\u03b8\u03b5\u03cd\u03b5\u03c4\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03cc\u03bb\u03b5\u03c2 \u03c4\u03b9\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03c9\u03bd \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ce\u03bd \u03b1\u03c5\u03c4\u03ce\u03bd \u03bb\u03ad\u03b3\u03b5\u03c4\u03b1\u03b9 \u03c4\u03b1\u03c5\u03c4\u03cc\u03c4\u03b7\u03c4\u03b1<\/strong>.<\/p>\n

\u039f\u03b9 \u03c0\u03b9\u03bf \u03b1\u03be\u03b9\u03bf\u03c3\u03b7\u03bc\u03b5\u03af\u03c9\u03c4\u03b5\u03c2 \u03c4\u03b1\u03c5\u03c4\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9:<\/p>\n

    \n
  • \"(\gra+\grb)^2=\gra^2+2\gra\grb+\grb^2\"<\/li>\n
  • \"(\gra-\grb)^2=\gra^2-2\gra\grb+\grb^2\"<\/li>\n
  • \"(\gra+\grb)(\gra-\grb)=\gra^2-\grb^2\"<\/li>\n
  • \"(\gra+\grb)^3=\gra^3+3\gra^2\grb+3\gra\grb^2+\grb^3\"<\/li>\n
  • \"(\gra-\grb)^3=\gra^3-3\gra^2\grb+3\gra\grb^2-\grb^3\"<\/li>\n
  • \"\gra^3+\grb^3=(\gra+\grb)(\gra^2-\gra\grb+\grb^2)\"<\/li>\n
  • \"\gra^3-\grb^3=(\gra-\grb)(\gra^2+\gra\grb+\grb^2)\"<\/li>\n
  • \"(\gra+\grb+\grg)^2=\gra^2+\grb^2+\grg^2+2\gra\grb+2\gra\grg+2\grb\grg\"<\/li>\n<\/ul>\n

     <\/p>\n

    \u03a0\u03bf\u03b9\u03b5\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03b2\u03b1\u03c3\u03b9\u03ba\u03cc\u03c4\u03b5\u03c1\u03b5\u03c2 \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf\u03b9 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7\u03c2;<\/strong><\/em><\/span><\/p>\n

    \u039f\u03b9 \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf\u03b9 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b5\u03be\u03ae\u03c2:<\/p>\n

    \u0395\u03c5\u03b8\u03b5\u03af\u03b1 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7<\/strong><\/p>\n

    \u039e\u03b5\u03ba\u03b9\u03bd\u03ac\u03bc\u03b5 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c5\u03c0\u03cc\u03b8\u03b5\u03c3\u03b7 (\u03b7 \u03bf\u03c0\u03bf\u03af\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03bb\u03b7\u03b8\u03ae\u03c2) \u03ba\u03b1\u03b9 \u03bc\u03b5 \u03b4\u03b9\u03b1\u03b4\u03bf\u03c7\u03b9\u03ba\u03ac \u03b2\u03ae\u03bc\u03b1\u03c4\u03b1 (\u03c0\u03c1\u03ac\u03be\u03b5\u03b9\u03c2 \u03ae \u03c3\u03b5\u03b9\u03c1\u03ac \u03bb\u03bf\u03b3\u03b9\u03ba\u03ce\u03bd (\u03b1\u03bb\u03b7\u03b8\u03ce\u03bd) \u03c0\u03c1\u03bf\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd) \u03ba\u03b1\u03c4\u03b1\u03bb\u03ae\u03b3\u03bf\u03c5\u03bc\u03b5 \u03c3\u03c4\u03bf \u03c3\u03c5\u03bc\u03c0\u03ad\u03c1\u03b1\u03c3\u03bc\u03b1.<\/p>\n

     <\/p>\n

    \u039d\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03b1<\/span><\/strong><\/em>\u03bd<\/strong> \"\gra + \grb + \grg = 0,\" \u03c4\u03cc\u03c4\u03b5<\/strong> \"\gra^3 + \grb^3 + \grg^3 = 3\gra\grb\grg\"<\/span><\/p>\n

     <\/p>\n

    \u0395\u03c0\u03b5\u03b9\u03b4\u03ae \u03b1 + \u03b2 + \u03b3 = 0, \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1 = -(\u03b2 + \u03b3) (\u03c3\u03c7\u03ad\u03c3\u03b7 1), \u03bf\u03c0\u03cc\u03c4\u03b5 \u03b8\u03b1 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5:<\/p>\n

      <\/span>   <\/span>\"\begin{align*}<\/p>\n

    \u03a0\u03b1\u03c1\u03b1\u03bb\u03bb\u03b1\u03b3\u03ad\u03c2 \u03c4\u03b7\u03c2 \u03b5\u03c5\u03b8\u03b5\u03af\u03b1\u03c2 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7\u03c2<\/strong><\/p>\n

      \n
    • \u0391\u03c1\u03c7\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03b1\u03c0\u03cc \u03c4\u03bf \u03ad\u03bd\u03b1 \u03bc\u03ad\u03bb\u03bf\u03c2 (\u03b1\u03c5\u03c4\u03cc \u03c0\u03bf\u03c5 \u03ad\u03c7\u03b5\u03b9 \u03c4\u03b9\u03c2 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03b5\u03c2 \u03c0\u03b1\u03c1\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03b9\u03c2), \u03ba\u03ac\u03bd\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b9\u03c2 \u03c0\u03c1\u03ac\u03be\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b9 \u03ba\u03b1\u03c4\u03b1\u03bb\u03ae\u03b3\u03bf\u03c5\u03bc\u03b5 \u03c3\u03c4\u03bf \u03ac\u03bb\u03bb\u03bf \u03bc\u03ad\u03bb\u03bf\u03c2.<\/li>\n<\/ul>\n

       <\/p>\n

      \u039d\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 <\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/em>\"(\gra+\grb)^2=\gra^2+2\gra\grb+\grb^2\"<\/p>\n

        <\/span>   <\/span>\"\begin{align*}<\/p>\n

        \n
      • \u039a\u03ac\u03bd\u03bf\u03c5\u03bc\u03b5 \u03c0\u03c1\u03ac\u03be\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b9 \u03c3\u03c4\u03b1 \u03b4\u03cd\u03bf \u03bc\u03ad\u03bb\u03b7 \u03c3\u03c5\u03b3\u03c7\u03c1\u03cc\u03bd\u03c9\u03c2 \u03ba\u03b1\u03b9 \u03bc\u03b5 \u03c4\u03b7 \u03c7\u03c1\u03ae\u03c3\u03b7 \u03b9\u03c3\u03bf\u03b4\u03c5\u03bd\u03b1\u03bc\u03b9\u03ce\u03bd \u03ba\u03b1\u03c4\u03b1\u03bb\u03ae\u03b3\u03bf\u03c5\u03bc\u03b5 \u03c3\u03b5 \u03bc\u03b9\u03b1 \u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c0\u03bf\u03c5 \u03c0\u03c1\u03bf\u03c6\u03b1\u03bd\u03ce\u03c2 \u03b1\u03bb\u03b7\u03b8\u03b5\u03cd\u03b5\u03b9.<\/li>\n<\/ul>\n

         <\/p>\n

        \u039d\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u00a0<\/span><\/strong><\/em>\"(\gra^2 + \grb^2)(x^2 + y^2) = (\gra x + \grb y)^2 + (\gra y - \grb x)^2\"<\/p>\n

          <\/span>   <\/span>\"\begin{align*}<\/p>\n

          \n
        • \u039b\u03cd\u03bd\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b7\u03bd \u03c5\u03c0\u03cc\u03b8\u03b5\u03c3\u03b7 \u03c9\u03c2 \u03c0\u03c1\u03bf\u03c2 \u03bc\u03b9\u03b1 \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ae \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd \u03b1\u03bd\u03c4\u03b9\u03ba\u03b1\u03b8\u03b9\u03c3\u03c4\u03bf\u03cd\u03bc\u03b5 \u03c3\u03c4\u03bf \u03ad\u03bd\u03b1 \u03ae \u03ba\u03b1\u03b9 \u03c3\u03c4\u03b1 \u03b4\u03cd\u03bf \u03bc\u03ad\u03bb\u03b7 \u03c4\u03b7\u03c2 \u03c4\u03b1\u03c5\u03c4\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2 \u03c0\u03bf\u03c5 \u03b8\u03ad\u03bb\u03bf\u03c5\u03bc\u03b5 \u03bd\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03bf\u03c5\u03bc\u03b5.<\/li>\n<\/ul>\n

           <\/p>\n

          \u0391\u03bd \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9<\/span><\/strong><\/em> \"\gra-\grb=3,\" \u03bd\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9<\/strong><\/em><\/span> \"3\gra-\grb^2-3\grb+2\gra\grb=\gra^2\"<\/p>\n

          \u0395\u03c0\u03b5\u03b9\u03b4\u03ae \"\gra-\grb=3,\" , \u03b5\u03af\u03bd\u03b1\u03b9 \"\gra=\grb+3,\" (\u03c3\u03c7\u03ad\u03c3\u03b7 1), \u03bf\u03c0\u03cc\u03c4\u03b5 \u03b8\u03b1 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5:<\/p>\n

            <\/span>   <\/span>\"\begin{align*}<\/p>\n

          A\u03c0\u03b1\u03b3\u03c9\u03b3\u03ae \u03c3\u03b5 \u03ac\u03c4\u03bf\u03c0\u03bf<\/strong><\/p>\n

          Y\u03c0\u03bf\u03b8\u03ad\u03c4\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03b4\u03b5\u03bd \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9 \u03b1\u03c5\u03c4\u03cc \u03c0\u03bf\u03c5 \u03b8\u03ad\u03bb\u03b1\u03bc\u03b5 \u03bd\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03bf\u03c5\u03bc\u03b5 \u03ba\u03b1\u03b9 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03ce\u03bd\u03c4\u03b1\u03c2 \u03b1\u03bb\u03b7\u03b8\u03b5\u03af\u03c2 \u03c0\u03c1\u03bf\u03c4\u03ac\u03c3\u03b5\u03b9\u03c2 \u03ba\u03b1\u03c4\u03b1\u03bb\u03ae\u03b3\u03bf\u03c5\u03bc\u03b5 \u03c3\u03b5 \u03ad\u03bd\u03b1 \u03c3\u03c5\u03bc\u03c0\u03ad\u03c1\u03b1\u03c3\u03bc\u03b1 \u03c0\u03bf\u03c5 \u03ad\u03c1\u03c7\u03b5\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03b1\u03bd\u03c4\u03af\u03b8\u03b5\u03c3\u03b7 \u03bc\u03b5 \u03b1\u03c5\u03c4\u03cc \u03c0\u03bf\u03c5 \u03b3\u03bd\u03c9\u03c1\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9. \u039f\u03b4\u03b7\u03b3\u03b7\u03b8\u03ae\u03ba\u03b1\u03bc\u03b5 \u03cc\u03c0\u03c9\u03c2 \u03bb\u03ad\u03bc\u03b5 \u03c3\u03b5 \u03ac\u03c4\u03bf\u03c0\u03bf<\/strong>.<\/p>\n

           <\/p>\n

          \u0391\u03bd<\/span><\/strong><\/em> \u03bf \"\gra^2\" \u03b5\u03af\u03bd\u03b1\u03b9 \u03ac\u03c1\u03c4\u03b9\u03bf\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2, \u03c4\u03cc\u03c4\u03b5 \u03bd\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03ba\u03b1\u03b9 \u03bf<\/span><\/strong><\/em> \"\gra\" \u03b5\u03af\u03bd\u03b1\u03b9 \u03ac\u03c1\u03c4\u03b9\u03bf\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2.<\/strong><\/em><\/span><\/p>\n

          \u0388\u03c3\u03c4\u03c9 \u03cc\u03c4\u03b9 \u03bf \u03b1 \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03ac\u03c1\u03c4\u03b9\u03bf\u03c2. \u03a4\u03cc\u03c4\u03b5 \u03bf \u03b1 \u03b8\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03b5\u03c1\u03b9\u03c4\u03c4\u03cc\u03c2, \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae \u03b8\u03b1 \u03ad\u03c7\u03b5\u03b9 \u03c4\u03b7 \u03bc\u03bf\u03c1\u03c6\u03ae<\/p>\n

          \u03b1 = 2\u03ba + 1, \u03cc\u03c0\u03bf\u03c5 \u03ba \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf\u03c2, \u03bf\u03c0\u03cc\u03c4\u03b5 \u03b8\u03b1 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5:<\/p>\n

            <\/span>   <\/span>\"\begin{align*}<\/p>\n

          \u0394\u03b7\u03bb\u03b1\u03b4\u03ae \"\gra^2 = 2\grl + 1,\quad \grl\in\zz,\", \u03c0\u03bf\u03c5 \u03c3\u03b7\u03bc\u03b1\u03af\u03bd\u03b5\u03b9 \u03cc\u03c4\u03b9 \u03bf \"\gra^2\" \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03b5\u03c1\u03b9\u03c4\u03c4\u03cc\u03c2. \u0391\u03c5\u03c4\u03cc \u03cc\u03bc\u03c9\u03c2 \u03ad\u03c1\u03c7\u03b5\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03b1\u03bd\u03c4\u03af\u03b8\u03b5\u03c3\u03b7 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c5\u03c0\u03cc\u03b8\u03b5\u03c3\u03b7 \u03cc\u03c4\u03b9 \u03bf \"α^2\" \u03b5\u03af\u03bd\u03b1\u03b9 \u03ac\u03c1\u03c4\u03b9\u03bf\u03c2. (\u03ac\u03c4\u03bf\u03c0\u03bf)<\/p>\n

          \u0395\u03c0\u03bf\u03bc\u03ad\u03bd\u03c9\u03c2, \u03b7 \u03c0\u03b1\u03c1\u03b1\u03b4\u03bf\u03c7\u03ae \u03cc\u03c4\u03b9 \u03b1 \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03ac\u03c1\u03c4\u03b9\u03bf\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bb\u03b1\u03bd\u03b8\u03b1\u03c3\u03bc\u03ad\u03bd\u03b7. \u0386\u03c1\u03b1 \u03bf \u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ac\u03c1\u03c4\u03b9\u03bf\u03c2.<\/p>\n

          \u039c\u03b5 \u03b1\u03bd\u03c4\u03b9\u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1<\/strong><\/p>\n

          \u0393\u03b9\u03b1 \u03bd\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03ad\u03bd\u03b1\u03c2 \u03b9\u03c3\u03c7\u03c5\u03c1\u03b9\u03c3\u03bc\u03cc\u03c2 \u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03ac\u03bd\u03c4\u03b1 \u03b1\u03bb\u03b7\u03b8\u03ae\u03c2<\/strong>, \u03b1\u03c1\u03ba\u03b5\u03af \u03bd\u03b1 \u03b2\u03c1\u03bf\u03cd\u03bc\u03b5 \u03ad\u03bd\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1 \u03b3\u03b9\u03b1 \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03bf \u03c3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03bf\u03c2 \u03b9\u03c3\u03c7\u03c5\u03c1\u03b9\u03c3\u03bc\u03cc\u03c2 \u03b4\u03b5\u03bd \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9 \u03ae, \u03cc\u03c0\u03c9\u03c2 \u03bb\u03ad\u03bc\u03b5, \u03b1\u03c1\u03ba\u03b5\u03af \u03bd\u03b1 \u03b2\u03c1\u03bf\u03cd\u03bc\u03b5 \u03ad\u03bd\u03b1 \u03b1\u03bd\u03c4\u03b9\u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1.<\/p>\n

           <\/p>\n

          \u039d\u03b1 \u03b5\u03be\u03b5\u03c4\u03ac\u03c3\u03b5\u03c4\u03b5 \u03b1\u03bd \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 \"\alpha > 0\" \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9 \"\gra^2 > \gra.\"<\/strong><\/em><\/span><\/p>\n

          \u0393\u03b9\u03b1 \"\gra=\dfrac{1}{2}>0\" \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 \"\gra^2=\dfrac{1}{4},\" \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae \"\gra^2<\gra\" \u03ac\u03c1\u03b1 \u03bf \u03b9\u03c3\u03c7\u03c5\u03c1\u03b9\u03c3\u03bc\u03cc\u03c2 \u03b4\u03b5\u03bd \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9.<\/p>\n

           <\/p>\n

          \n

          \u0392\u03b9\u03b2\u03bb\u03b9\u03bf\u03b3\u03c1\u03b1\u03c6\u03af\u03b1:<\/strong> \u0391\u039b\u0393\u0395\u0392\u03a1\u0391 \u039a\u0391\u0399 \u03a3\u03a4\u039f\u0399\u03a7\u0395\u038a\u0391 \u03a0\u0399\u0398\u0391\u039d\u039f\u03a4\u0389\u03a4\u03a9\u039d \u0391\u00b4 \u03c4\u03ac\u03be\u03b7\u03c2 \u0393\u03b5\u03bd\u03b9\u03ba\u03bf\u03cd \u039b\u03c5\u03ba\u03b5\u03af\u03bf\u03c5, \u0391\u03bd\u03b4\u03c1\u03b5\u03b1\u03b4\u03ac\u03ba\u03b7\u03c2 \u03a3\u03c4\u03c5\u03bb\u03b9\u03b1\u03bd\u03cc\u03c2, \u039a\u03b1\u03c4\u03c3\u03b1\u03c1\u03b3\u03cd\u03c1\u03b7\u03c2 \u0392\u03b1\u03c3\u03af\u03bb\u03b5\u03b9\u03bf\u03c2, \u039c\u03ad\u03c4\u03b7\u03c2 \u03a3\u03c4\u03ad\u03c6\u03b1\u03bd\u03bf\u03c2, \u039c\u03c0\u03c1\u03bf\u03c5\u03c7\u03bf\u03cd\u03c4\u03b1\u03c2 \u039a\u03c9\u03bd\/\u03bd\u03bf\u03c2, \u03a0\u03b1\u03c0\u03b1\u03c3\u03c4\u03b1\u03c5\u03c1\u03af\u03b4\u03b7\u03c2 \u03a3\u03c4\u03b1\u03cd\u03c1\u03bf\u03c2,\u03a0\u03bf\u03bb\u03cd\u03b6\u03bf\u03c2 \u0393\u03b5\u03ce\u03c1\u03b3\u03b9\u03bf\u03c2, \u03a5.\u03a0\u0391\u0399.\u0398.<\/p>\n

          Creative Commons \u0391\u03bd\u03b1\u03c6\u03bf\u03c1\u03ac \u0394\u03b7\u03bc\u03b9\u03bf\u03c5\u03c1\u03b3\u03bf\u03cd – \u039c\u03b7 \u0395\u03bc\u03c0\u03bf\u03c1\u03b9\u03ba\u03ae \u03a7\u03c1\u03ae\u03c3\u03b7 – \u03a0\u03b1\u03c1\u03cc\u03bc\u03bf\u03b9\u03b1 \u0394\u03b9\u03b1\u03bd\u03bf\u03bc\u03ae 4.0 \u0394\u03b9\u03b5\u03b8\u03bd\u03ad\u03c2<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

          \u03a3\u03b7\u03bc\u03b5\u03b9\u03ce\u03c3\u03b5\u03b9\u03c2 \u0398\u03b5\u03c9\u03c1\u03af\u03b1\u03c2   \u03a0\u03bf\u03b9\u03b5\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03c0\u03b9\u03bf \u03b1\u03be\u03b9\u03bf\u03c3\u03b7\u03bc\u03b5\u03af\u03c9\u03c4\u03b5\u03c2 \u03c4\u03b1\u03c5\u03c4\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2; \u039a\u03ac\u03b8\u03b5 \u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c0\u03bf\u03c5 \u03c0\u03b5\u03c1\u03b9\u03ad\u03c7\u03b5\u03b9 \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ad\u03c2 \u03ba\u03b1\u03b9 \u03b5\u03c0\u03b1\u03bb\u03b7\u03b8\u03b5\u03cd\u03b5\u03c4\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03cc\u03bb\u03b5\u03c2 \u03c4\u03b9\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03c9\u03bd \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ce\u03bd \u03b1\u03c5\u03c4\u03ce\u03bd \u03bb\u03ad\u03b3\u03b5\u03c4\u03b1\u03b9 \u03c4\u03b1\u03c5\u03c4\u03cc\u03c4\u03b7\u03c4\u03b1. \u039f\u03b9 \u03c0\u03b9\u03bf \u03b1\u03be\u03b9\u03bf\u03c3\u03b7\u03bc\u03b5\u03af\u03c9\u03c4\u03b5\u03c2 \u03c4\u03b1\u03c5\u03c4\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9:   \u03a0\u03bf\u03b9\u03b5\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03b2\u03b1\u03c3\u03b9\u03ba\u03cc\u03c4\u03b5\u03c1\u03b5\u03c2 \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf\u03b9 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7\u03c2; \u039f\u03b9 \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf\u03b9 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b5\u03be\u03ae\u03c2: \u0395\u03c5\u03b8\u03b5\u03af\u03b1 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 \u039e\u03b5\u03ba\u03b9\u03bd\u03ac\u03bc\u03b5 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c5\u03c0\u03cc\u03b8\u03b5\u03c3\u03b7 (\u03b7…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[],"class_list":["post-1238","post","type-post","status-publish","format-standard","hentry","category-2---"],"featured_image_src":null,"author_info":{"display_name":"admin","author_link":"https:\/\/gbelentzas.sites.sch.gr\/?author=1"},"yoast_head":"\n2.1 \u039f\u03b9 \u03c0\u03c1\u03ac\u03be\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b9 \u03bf\u03b9 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03ad\u03c2 \u03c4\u03bf\u03c5\u03c2 - \u0391\u03be\u03b9\u03bf\u03c3\u03b7\u03bc\u03b5\u03af\u03c9\u03c4\u03b5\u03c2 \u03a4\u03b1\u03c5\u03c4\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 (\u0398\u03b5\u03c9\u03c1\u03af\u03b1) - MathsEdu.gr<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/gbelentzas.sites.sch.gr\/?p=1238\" \/>\n<meta property=\"og:locale\" content=\"el_GR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"2.1 \u039f\u03b9 \u03c0\u03c1\u03ac\u03be\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b9 \u03bf\u03b9 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03ad\u03c2 \u03c4\u03bf\u03c5\u03c2 - \u0391\u03be\u03b9\u03bf\u03c3\u03b7\u03bc\u03b5\u03af\u03c9\u03c4\u03b5\u03c2 \u03a4\u03b1\u03c5\u03c4\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 (\u0398\u03b5\u03c9\u03c1\u03af\u03b1) - MathsEdu.gr\" \/>\n<meta property=\"og:description\" content=\"\u03a3\u03b7\u03bc\u03b5\u03b9\u03ce\u03c3\u03b5\u03b9\u03c2 \u0398\u03b5\u03c9\u03c1\u03af\u03b1\u03c2   \u03a0\u03bf\u03b9\u03b5\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03c0\u03b9\u03bf \u03b1\u03be\u03b9\u03bf\u03c3\u03b7\u03bc\u03b5\u03af\u03c9\u03c4\u03b5\u03c2 \u03c4\u03b1\u03c5\u03c4\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2; \u039a\u03ac\u03b8\u03b5 \u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c0\u03bf\u03c5 \u03c0\u03b5\u03c1\u03b9\u03ad\u03c7\u03b5\u03b9 \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ad\u03c2 \u03ba\u03b1\u03b9 \u03b5\u03c0\u03b1\u03bb\u03b7\u03b8\u03b5\u03cd\u03b5\u03c4\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03cc\u03bb\u03b5\u03c2 \u03c4\u03b9\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03c9\u03bd \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ce\u03bd \u03b1\u03c5\u03c4\u03ce\u03bd \u03bb\u03ad\u03b3\u03b5\u03c4\u03b1\u03b9 \u03c4\u03b1\u03c5\u03c4\u03cc\u03c4\u03b7\u03c4\u03b1. \u039f\u03b9 \u03c0\u03b9\u03bf \u03b1\u03be\u03b9\u03bf\u03c3\u03b7\u03bc\u03b5\u03af\u03c9\u03c4\u03b5\u03c2 \u03c4\u03b1\u03c5\u03c4\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9:   \u03a0\u03bf\u03b9\u03b5\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03b2\u03b1\u03c3\u03b9\u03ba\u03cc\u03c4\u03b5\u03c1\u03b5\u03c2 \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf\u03b9 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7\u03c2; \u039f\u03b9 \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf\u03b9 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b5\u03be\u03ae\u03c2: \u0395\u03c5\u03b8\u03b5\u03af\u03b1 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 \u039e\u03b5\u03ba\u03b9\u03bd\u03ac\u03bc\u03b5 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c5\u03c0\u03cc\u03b8\u03b5\u03c3\u03b7 (\u03b7...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/gbelentzas.sites.sch.gr\/?p=1238\" \/>\n<meta property=\"og:site_name\" content=\"MathsEdu.gr\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/MathsEdu.gr\" \/>\n<meta property=\"article:published_time\" content=\"2024-09-10T18:31:16+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-09-14T05:34:46+00:00\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u03a3\u03c5\u03bd\u03c4\u03ac\u03c7\u03b8\u03b7\u03ba\u03b5 \u03b1\u03c0\u03cc\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u0395\u03ba\u03c4\u03b9\u03bc\u03ce\u03bc\u03b5\u03bd\u03bf\u03c2 \u03c7\u03c1\u03cc\u03bd\u03bf\u03c2 \u03b1\u03bd\u03ac\u03b3\u03bd\u03c9\u03c3\u03b7\u03c2\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 \u03bb\u03b5\u03c0\u03c4\u03ac\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/gbelentzas.sites.sch.gr\\\/?p=1238#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/gbelentzas.sites.sch.gr\\\/?p=1238\"},\"author\":{\"name\":\"admin\",\"@id\":\"https:\\\/\\\/gbelentzas.sites.sch.gr\\\/#\\\/schema\\\/person\\\/511115b6820d1a71ade6791721485e15\"},\"headline\":\"2.1 \u039f\u03b9 \u03c0\u03c1\u03ac\u03be\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b9 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