Simplify:$ \left(x^{4}+\frac{1}{x^{4}}\right)\left(x+\frac{1}{x}\right) $

Given:

\( \left(x^{4}+\frac{1}{x^{4}}\right)\left(x+\frac{1}{x}\right) \)

To do:

We have to find the value of \( \left(x^{4}+\frac{1}{x^{4}}\right)\left(x+\frac{1}{x}\right) \).

Solution:

$(x^{4}+\frac{1}{x^{4}})(x+\frac{1}{x})=x^4(x+\frac{1}{x})+\frac{1}{x^{4}}(x+\frac{1}{x})$

$=x^{4+1}+x^{4-1}+\frac{1}{x^{4-1}}+\frac{1}{x^{4+1}}$

$=x^5+x^3+\frac{1}{x^{3}}+\frac{1}{x^{5}}$

Hence, $(x^{4}+\frac{1}{x^{4}})(x+\frac{1}{x})=x^5+x^3+\frac{1}{x^{3}}+\frac{1}{x^{5}}$.

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Updated on: 10-Oct-2022

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