Question

value of (a^1/8 + a^-1/8) (a^1/8 - a^-1/8) (a^1/4 + a^-1/4) (a^1/2 + a^-1/2) is?
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Answer 1

Answer

a-1/a

Step-by-step explanation

(a^1/8+a^-1/8)(a^1/8-a^-1/8)(a^1/4+a^-1/4)(a^1/2+a^-1/2)

=[(a^1/8)^2-(a^-1/8)^2 ](a^1/4+a^-1/4)(a^1/2+a^-1/2)

=(a^1/4-a^-1/4)(a^1/4+a^-1/4)(a^1/2+a^-1/2)

=[(a^1/4)^2-(a^-1/4)^2](a^1/2+a^-1/2)

=(a^1/2-a^-1/2)(a^1/2+a^-1/2)

=(a^1/2)^2-(a^-1/2)^2

=a-1/a