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\( \Large \left(x+\frac{1}{x}\right) \left(x-\frac{1}{x}\right) \left(x^{2}+\frac{1}{x^{2}}-1\right) \left(x^{2}+\frac{1}{x^{2}+1}\right) \) is equal to:

A) \( \Large x^{6}+\frac{1}{x^{6}} \)
B) \( \Large x^{8}+\frac{1}{x^{8}} \)
C) \( \Large x^{8}-\frac{1}{x^{8}} \)
D) \( \Large x^{6}-\frac{1}{x^{6}} \)

Correct Answer:




D) \( \Large x^{6}-\frac{1}{x^{6}} \)

Description for Correct answer:
\( \Large \left(x+\frac{1}{x}\right) \left(x-\frac{1}{x}\right) \left(x^{2}+\frac{1}{x^{2}}-1\right) \left(x^{2}+\frac{1}{x^{2}}+1\right) \)

= \( \Large \left(x+\frac{1}{x}\right) \left(x^{2}+\frac{1}{x^{2}}-1\right) \left(x-\frac{1}{x}\right) \left(x^{2}+\frac{1}{x^{2}}+1\right) \)

Because, \( \Large \left(A+B\right) \left(A^{2}-AB+B^{2}\right)=A^{3}+B^{3} \)

\( \Large \left(A-B\right) \left(A^{2}+AB+B^{2}\right)=A^{3}-b^{3} \)

=\( \Large \left(x^{3}+\frac{1}{x^{3}}\right) \left(x^{3}-\frac{1}{x^{3

}}\right) = x^{6}-\frac{1}{x^{6}} \)

Part of solved Elementary Mathematics questions and answers : >> Elementary Mathematics

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