Question

If $x+\frac{1}{x}=5,then{x}^6+\frac{1}{x^6}$ is

• A. $12098$
• B. $12048$
• C. $14062$
• D. $12092$

Answer 1

The correct option is A $12098$

x + $\frac{1}{x}$ = $5$
On cubing, we get
$x^3+\frac{1}{x^3}+3(x+\frac{1}{x})=125$
$x^3+\frac{1}{x^3}+3\times 5=125\Rightarrow x^3+\frac{1}{x^3}=110$
Squaring both the sides, we get
$x^6+\frac{1}{x^6}+2=12100$
Hence, $x^6+\frac{1}{x^6}=121002=12098$