Question

Se x+1/x=b, calcule x+1/x²

Answer 1

$x+\dfrac{1}{x}=b\\ \\ \\ b^{2}=\left(x+\dfrac{1}{x} \right )^{2}\\ \\ =x^{2}+2\cdot \diagup\!\!\!\! x \cdot \dfrac{1}{\diagup\!\!\!\! x}+\left(\dfrac{1}{x} \right )^{2}\\ \\ =x^{2}+2+\dfrac{1}{x^{2}}\\ \\ =x^{2}+\dfrac{1}{x^{2}}+2\\ \\ \\ b^{2}=x^{2}+\dfrac{1}{x^{2}}+2\\ \\ \boxed{x^{2}+\dfrac{1}{x^{2}}=b^{2}-2}$

Answer 2

Resposta:

Explicação passo-a-passo: