Question

Sendo( x + 1/x)² = 20, qual é o valor de 1/x² + x²?

Answer 1

Temos que:

$(a+b)^2 = a^2 + 2ab + b^2$

Logo:

$(x + \frac{1}{x} )^2 = 20 \to x^2 + 2 \cdot x \cdot \frac{1}{x} + \frac{1}{x^2} =20 \to x^2 + 2 +\frac{1}{x^2} = 20 \\ \\ x^2 + \frac{1}{x^2} = 20 - 2 \to x^2 + \frac{1}{x^2} = 18$