Question

If x+(1/x)=5, then evaluate x6+(1/x6)

Answer 1

Answer:

$x^6+\frac{1}{x^6}=12098$

Step-by-step explanation:

Given:

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

squaring on both sides

$x^2+\frac{1}{x^2}+2=25$

$x^2+\frac{1}{x^2}-23=0$

Using the following identity

$\textbf{If a+b+c=0, then } \bf\,a^3+b^3+c^3=3xyz$

$x^6+\frac{1}{x^6}+(-23)^3=3x^2(\frac{1}{x^2})(-23)$

$x^6+\frac{1}{x^6}-12167=-69$

$x^6+\frac{1}{x^6}=12167-69$

$\implies\boxed{\bf\,x^6+\frac{1}{x^6}=12098}$

Answer 2

Answer:

12098

Step-by-step explanation: