Question

If x² + 1/x² =11, find the value of a) x- 1/x b) x⁴ + 1/x⁴ please give full and correct answer either i will report that i am giving 30 points​

Answer 1

Given equation.

$\implies x^{2}+\dfrac{1}{x^{2}}=11$

Subtract 2.

$\implies x^{2}-2+\dfrac{1}{x^{2}}=9$

$\implies\left(x-\dfrac{1}{x}\right)^{2}=3^{2}$

We get  $x-\dfrac{1}{x}=3$or $x-\dfrac{1}{x}=-3$.

Note: If the question requires one answer it will be $x-\dfrac{1}{x}=3$, as this equation involves square root.

Given equation.

$\implies x^{2}+\dfrac{1}{x^{2}}=11$

Squaring both sides

$\implies x^{4}+2+\dfrac{1}{x^{4}}=121$

$\implies x^{4}+\dfrac{1}{x^{4}}=119$

Hope this helps!