SSC CGL 17 Aug 2021 Shift 3 Paper

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Question : 72 of 100

Marks: +1, -0

Simplify the following expression

\;{108 × 108 × 108-92 × 92 × 92}/{108 × 108+92 × 92+108 × 92}

108 × 10

16
$-1$
1
200

Solution:

Given expression,

\;{108 × 108 × 108-92 × 92 × 92}/{108 × 108+92 × 92+108 × 92}

We know that,

a^{3}-b^{3}=(a-b)(a^{2}+b^{2}+a b)

Here,

a=108, b=92

\;{(108)^{3}-(92)^{3}}/{(108)^{2}+(92)^{2}+108 × 92}

\;\; =\;{(108-92)[(108)^{2}+(92)^{2}+108 × 92]}/{[(108)^{2}+(92)^{2}+108 × 92]}

\;\; =(108-92)=16

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