Question

Dado que x+(1/x)=4 obtenha o valor numérico de x^2+(1/x^2)

Answer 1

Boa tarde!

Dado:
$\displaystyle{x+\frac{1}{x}=4}\\\displaystyle{\left(x+\frac{1}{x}\right)^2=4^2}\\\displaystyle{x^2+2x\frac{1}{x}+\left(\frac{1}{x}\right)^2=16}\\\displaystyle{x^2+2+\frac{1}{x^2}=16}\\\displaystyle{x^2+\frac{1}{x^2}=16-2}\\\boxed{x^2+\frac{1}{x^2}=14}$

Espero ter ajudado!