Vamos lá.

(y² + 1)/y² = 5

y² + 1 = 5y²

4y² = 1

y² = 1/4

y = 1/2

(y + 1/y)² = (1/2 + 2)² = 25/4 <--- Esta é a resposta.

É isso aí.

Deu pra entender bem?

Ok?

Mestre Albert

Verified answer

[tex]\displaystyle \sf y^2+\frac{1}{y^2} = 5 \ \ ; \ \ \left(y+\frac{1}{y}\right)^2 = \ ? \\\\\\ \text{Desenvolvendo }: \\\\ \left(y+\frac{1}{y}\right)^2 = y^2+2\cdot y\cdot \frac{1}{y} + \frac{1}{y^2} \\\\\\ \left(y+\frac{1}{y}\right)^2 = \underbrace{\sf y^2+\frac{1}{y^2}}_{5}+2 \\\\\\ \left(y+\frac{1}{y}\right)^2 = 5+2 \\\\\\ \boxed{\sf \left(y+\frac{1}{y}\right)^2 = 7\ }\checkmark[/tex]