Question

Sendo x²+1/x²=5, calcule o valor de: (x+1/x)²

Answer 1

Pelo enunciado, $x^2+\dfrac{1}{x^2}=5$

Veja que:

$\left(x+\dfrac{1}{x}\right)^2=x^2+2x\cdot\dfrac{1}{x}+\left(\dfrac{1}{x}\right)^2=x^2+2+\dfrac{1}{x^2}=5+2=7$