Question

Se x² + 1/x₂ =2², então o valor de x⁴ + 1/x⁴ é:

Answer 1

$x^{2}+\dfrac{1}{x^{2}}=2^{2}=4$

Elevando os dois lados da equação ao quadrado:

$\left(x^{2}+\dfrac{1}{x^{2}}\right)^{2}=4^{2}\\\\\\(x^{2})^{2}+2\cdot x^{2}\cdot\dfrac{1}{x^{2}}+\left[\dfrac{1}{x^{2}}\right]^{2}}\right=16\\\\\\x^{4}+2\cdot1+\dfrac{1}{x^{4}}=16\\\\\\x^{4}+\dfrac{1}{x^{4}}=16-2\\\\\\\boxed{\boxed{x^{4}+\dfrac{1}{x^{4}}=14}}$