Question

find the following product using suitable identities:-
(x+1/x)(x-1/x)(x sq+1/x sq)(x sq 4+1/x)​

Answer 1

${\bold{\underline{\red{\sf{Answer:}}}}}$${\boxed{\bold{\sf{{x}^{8}-\frac{1}{{x}^{8}}}}}}$

${\bold{\huge{\underline{\blue{\sf{Given:}}}}}}$

${\bold{\sf{(x+\frac{1}{x})(x-\frac{1}{x})(x²+\frac{1}{x²})(x⁴+\frac{1}{x⁴})}}}$

${\bold{\huge{\underline{\pink{\sf{To \: Find:}}}}}}$

${\bold{\sf{Find \: the \: product}}}$

${\bold{\huge{\underline{\orange{\sf{Formula:}}}}}}$

${\boxed{\sf{(a+b)(a-b)=a²-b²}}}$

${\bold{\huge{\underline{\green{\sf{Solution:}}}}}}$

${\bold{\sf{(x+\frac{1}{x})(x-\frac{1}{x})(x²+\frac{1}{x²})(x⁴+\frac{1}{x⁴})}}}$

${\bold{\sf{=(x²-\frac{1}{x²})(x²+\frac{1}{x²})(x⁴+\frac{1}{x⁴})}}}$

${\bold{\sf{=(x⁴-\frac{1}{x⁴})(x⁴+\frac{1}{x⁴})}}}$

${\bold{\sf{=}}}$${\boxed{\bold{\sf{{x}^{8}-\frac{1}{{x}^{8}}}}}}$

Answer 2

x^8 - (1/x^8)

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