Question

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

• A. 190
• B. 180
• C. 193
• D. 194

Answer 1

The correct option is D 194

Given,$x+\frac{1}{x}=4$
On squaring both sides, we get
$x^2+\frac{1}{x^2}+2\times x\times \frac{1}{x}=16$
$\Rightarrow x^2+\frac{1}{x^2}+2=25$
$\Rightarrow x^2+\frac{1}{x^2}=14$
Again on squaring both sides, we get
$\Rightarrow x^4+\frac{1}{x^4}+2\times x^2\times \frac{1}{x^2}=196$
$\Rightarrow x^4+\frac{1}{x^4}+2=196$
$\Rightarrow x^4+\frac{1}{x^4}=194$
Option D is correct.