Question

If $x+\frac{1}{x}=7$, then find the value of $x^4+\frac{1}{x^4}$

• A. $2207$
• B. $2209$
• C. $2232$
• D. $2294$

Answer 1

The correct option is A $2207$

We have, $x+\frac{1}{x}=7$

Squaring both sides, we get

$(x+\frac{1}{x}{)}^2=7^2$

$\Rightarrow x^2+\frac{1}{x^2}+2\times x\times \frac{1}{x}=49[\because (a+b{)}^2=a^2+b^2+2ab]$

$\Rightarrow x^2+\frac{1}{x^2}=47$

Again Squaring both sides, we get

$(x^2+\frac{1}{x^2}{)}^2={47}^2$

$\Rightarrow x^4+\frac{1}{x^4}+2\times x^2\times \frac{1}{x^2}=2209$

$\Rightarrow x^4+\frac{1}{x^4}=2207$

So, $\text{A}$ is the correct option.