Question

(PUC Rio) Se x²(1 – y)² = y²(1 – x)² e x ≠ y, então x + y será

Answer 1

${x}^{2}{(1-y)}^{2}={y}^{2}{(1-x)}^{2}\:x\ne\,y$

$\dfrac{{x}^{2}}{{y}^{2}}=\dfrac{{(1-x)}^{2}}{{(1-y)}^{2}}$

$\dfrac{{x}^{2}}{{y}^{2}}=\dfrac{1-2x+{x}^{2}}{1-2y+{y}^{2}}$

${x}^{2}-2{x}^{2}y+\cancel{{x}^{2}{y}^{2}}={y}^{2}-2x{y}^{2}+\cancel{{x}^{2}{y}^{2}}$

${x}^{2}-{y}^{2}=2{x}^{2}y-2x{y}^{2}$

$(x+y)\cancel{(x-y)}=2xy\cancel{(x-y)}$

$\boxed{\boxed{\mathsf{x+y=2xy}}}$