Question

$( \frac{x}{y} + \frac{y}{x}) {}^{2}$
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Answer 1

Resposta:

x²/y²+y²/x²+2

Explicação passo-a-passo:

(x/y+y/x)²= (x/y)²+2.(x/y).(y/x)+(y/x)²

(x/y+y/x)²= x²/y²+2.(1) +y²/x²

(x/y+y/x)²= x²/y²+y²/x²+2

Answer 2

Boa noite!

$(\frac{x}{y} + \frac{y}{x} )^2\\\\(\frac{x.x+y.y}{xy} )^2\\\\(\frac{x^2+y^2}{xy} )^2\\\\(\frac{x^2+y^2}{xy} ).(\frac{x^2+y^2}{xy} )\\\\(\frac{x^2.x^2+x^2.y^2+x^2.y^2+y^2.y^2}{x.x.y.y} )\\\\{(\frac{x^4+2x^2y^2+y^4}{x^2y^2} ) \rightarrow \frac{x^2}{y^2}+\frac{y^2}{x^2}} +2$

Portanto o valor final é:

$\frac{x^2}{y^2}+\frac{y^2}{x^2}} +2$