Question

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

Answer 1

$(x-\frac{1}{x})^2=x^2-2(x)(\frac{1}{x})+(\frac{1}{x})^2=\\\\ =x^2-2+\frac{1}{x^2}=\\\\ =x^2+\frac{1}{x^2}-2=\\\\ Como \ temos \ x^2+\frac{1}{x^2}=5\\\\ =5-2=3$