Question

dado que x + (1/x)=3, obtenha o valor numérico de x² + (1/x²)

Answer 1

$x^2 + \dfrac{1}{x^2} = \\\\ = x^2 + x^{-2}\\\\ = x(x+x^{-1}) \\\\ = x\left(x+\dfrac{1}{x}\right)\\\\\\ mas\:\: x+\dfrac{1}{x} = 3\\\\ =x \cdot 3\\\\ = 3x$