Question

Sendo A=(x + 1/x)² = 12, determine 1/x² + x².

Answer 1

$\left(x+\dfrac1x\right)^2=12\\\\x^2+2(x)\left(\dfrac1x\right)+\left(\dfrac1x\right)^2=12\\\\\\x^2+2+\dfrac{1}{x^2}=12\\\\x^2+\dfrac{1}{x^2}=12-2\\\\\\x^2+\dfrac{1}{x^2}=10$