Question

if 2(x2+y2)=(x+y)2 then show that x=y​

Answer 1

Answer:

$\:given \: that \\ \: \: 2(x2+ y2) = (x+ y)2 \\ to \: show \: that \: (x = y) \\ \\ now \\ 2(x2 + y2) = (x + y)2 \\( 2x2 + 2y2) = (x2 + y2 + 2xy) \\ (2x2 - x2 + 2y2 - y2) = 2xy \\ (x2 + y2) = 2xy \\ (x2 + y2 - 2xy) = 0 \\ (x - y )2 = 0 \\ (x - y) = \sqrt{0} \\(x - y ) = 0 \\ x = y \\ we \: know \: that \\ (x - y)2 = (x2 + y2 - 2xy) \\ (x + y)2 = (x2 + y2 + 2xy)$

hence proved (x=y)