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  4. If x+(1/x)=9, then the value of x4+(1/x4) is equal to

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Q. If $x+\frac{1}{x}=9$, then the value of $x^4+\frac{1}{x^4}$ is equal to __

Polynomials

Solution:

$x+\frac{1}{x}=9$
Squaring both sides,
$ \left(x+\frac{1}{x}\right)^2=81 $
$ \Rightarrow x^2+\frac{1}{x^2}+2 x^2 \frac{1}{x^2}=81$
$ \Rightarrow x^2+\frac{1}{x^2}=79$
Squaring again on both sides,
$ \left(x^2+\frac{1}{x^2}\right)^2=6241 $
$ \Rightarrow x^4+\frac{1}{x^4}+2 \cdot \frac{1}{x^2} \cdot x^2=6241$
$ \Rightarrow x^4+\frac{1}{x^4}=6239$