Question

$2(x {}^{2} + y {}^{2} ) = (x + y) {}^{2} then \: \:x = y \: prove$

Answer 1

Heya!!!

2x² + 2y² = x² + y² + 2xy

2 = 2xy

xy = 1..... equation 1

A.M ≥ G.M

x + y = 2 .... equation 2


x + 1 / x = 2

x² -2x + 1 = 0

x² - 1x - 1x + 1 = 0

x ( x - 1 ) - 1 ( x - 1 ) = 0

x = 1

For x = 1 y = 1

Therefore x = y. hence proved.