Question

sabendo que x+1/x = 14, então calcule o valor da expressão x^2+1/x^2

Answer 1

Olá Pérola!

$\\ \mathsf{x^2 + \frac{1}{x^2} =} \\\\ \mathsf{x^2 + 2 + \frac{1}{x^2} - 2 =} \\\\ \mathsf{\left(x^2+2\cdot x\cdot\frac{1}{x}+\frac{1}{x^2}\right)-2=} \\\\ \mathsf{\left (x + \frac{1}{x} \right )^2 - 2 =} \\\\ \mathsf{(14)^2 - 2 =} \\\\ \mathsf{196 - 2 =} \\\\ \boxed{\mathsf{194}}$