SSC CGL 18 Aug 2021 Shift 3 Paper

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Question : 71 of 100

Marks: +1, -0

If

a^{3}-b^{3}=2349

and

(a-b)=9

, then

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

is equal to

280
244
261
229

Solution:

Given,

a^{3}-b^{3}=2349

and

(a-b)=9

We know that,

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

⇒ \;\; 2349=9(a^{2}+b^{2}+a b)

⇒ \;\; (a^{2}+b^{2}+a b)=261

\;\text " Then, "\;(a+b)^{2}-a b

\;\;\; =a^{2}+b^{2}+2 a b-a b

\;\;\; [ ∵ (a+b)^{2}=a^{2}+b^{2}+2 a b]

∴ (a+b)^{2}-a b=a^{2}+b^{2}+a b=261

.

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