Question

If $x^4+\frac{1}{x^4}=727$, then $x-\frac{1}{x}$ is equal to

• A. $5$
• B. $\sqrt{29}$
• C. $25$
• D. $27$

Answer 1

The correct option is A $5$

$x^4+\frac{1}{x^4}=727$

Adding $2$ on both sides, we get

$x^4+\frac{1}{x^4}+2\times x^2\times \frac{1}{x^2}=727+2$

$\Rightarrow {(x^2+\frac{1}{x^2})}^2={27}^2$

Taking square root both sides, we get

$x^2+\frac{1}{x^2}=27$

Subtracting $2$ from both sides, we get

$x^2+\frac{1}{x^2}-2\times x\times \frac{1}{x}=27-2$

$\Rightarrow {(x-\frac{1}{x})}^2=5^2$

Taking square root on both sides, we get

$x-\frac{1}{x}=5$

Hence, option A.