Question

Sabendo que x^2+y^2=90 e xy=25 calcule

Answer 1

Olá,

$\tt \large{ \boxed{ \boxed{ \tt(x - y {)}^{2} = 40}}}$

Solução

$\tt \: (x - y {)}^{2} = (x - y)(x - y) \\ \\ \tt \: (x - y {)}^{2} = {x}^{2} - xy - xy + {y}^{2} \\ \\ \tt \: (x - y {)}^{2} = {x}^{2} - 2xy + {y}^{2} \\ \\ \tt \: (x - y {)}^{2} = {x}^{2} + {y}^{2} - 2xy \\ \\ \tt \: (x - y {)}^{2} = \overbrace{ {x}^{2} + {y}^{2} }^{90} - 2 \cdot \underbrace{xy}_{25} \\ \\ \tt(x - y {)}^{2} = 90 - 2 \cdot25 \\ \\ \tt(x - y {)}^{2} = 90 - 50 \\ \\ \tt(x - {y)}^{2} = 40$