Question

sendo x2+1/x2=5, calcule o valor de (x-1/x)2

Answer 1

$\left(x-\dfrac{1}{x}\right)^{2}=x^{2}-2\cdot x\cdot\dfrac{1}{x}+\left(\dfrac{1}{x}\right)^{2}\\\\\\\left(x-\dfrac{1}{x}\right)^{2}=x^{2}-2+\dfrac{1}{x^{2}}\\\\\\\left(x-\dfrac{1}{x}\right)^{2}=x^{2}+\dfrac{1}{x^{2}}-2\\\\\\\left(x-\dfrac{1}{x}\right)^{2}=5-2\\\\\\\boxed{\boxed{\left(x-\dfrac{1}{x}\right)^{2}=3}}$