Question

Find the value of (x-1/x)(x^2+1/x^2 )(x+1/x)

Answer 1

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Here is u r Ans ➡

✨
$= (x - \frac{1}{x} )(x {}^{2} + \frac{1}{x {}^{2} } )(x + \frac{1}{x})$

$= \frac{x {}^{2} - 1}{ x } \times \frac{x {}^{4} + 1 }{x {}^{2} } \times \frac{x {}^{2} + 1}{x}$

$= \frac{(x {}^{2} - 1) \times (x {}^{4} + 1) \times (x {}^{2} + 1)}{x {}^{4} }$
$= using \: > \: (a - b)(a + b) = a {}^{2} - b {}^{2}$

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

$= \frac{x {}^{8} - 1}{x {}^{4} }$
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Answer 2

(x - 1/x) (x + 1/x) = x² - 1/x²

(x² - 1/x²) (x² + 1/x²)

x⁴  -  1/x⁴