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ข้อความเดิมเขียนโดยคุณ Doraemon_kup

ผมทำแบบนี้ได้ป่าว _kup
$ x + y + z = 2$

$ (x + y + z)^{2} = 2^{2} $

$ x^{2} + y^{2} + z^{2} + 2( xy +yz + zx ) = 4$

$ (x^{2} + y^{2} + z^{2}) + 2(xy +yz + zx) = 4$

$ 4 + 2(xy +yz + zx) = 4 $

$ 2(xy +yz + zx) = 0$

$ xy +yz + zx = 0 ---(1)$

$ (xy +yz + zx)^{2} = 0$

$ (xy)^{2} + (yz)^{2} + (zx)^{2} + 2(x^{2}yz + xy^{2}z + xyz^{2}) = 0$

$ (xy)^{2} + (yz)^{2} + (zx)^{2} = - 2(x^{2}yz + xy^{2}z + xyz^{2})$

$ (xy)^{2} + (yz)^{2} + (zx)^{2} = - 2(xyz)(x + y + z)$

$ (xy)^{2} + (yz)^{2} + (zx)^{2} = - 2(-3)(2) $

$= 12$

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