SSC CGL 17 Aug 2021 Shift 1 Paper

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Question : 72 of 100

Marks: +1, -0

If

a^{2}+c^{2}+17=2(a-8 b-2 b^{2})

, then what is the value of

(a^{3}+b^{3}+c^{3}) ?

$-7$
9
10
$-4$

Solution:

Given,

a^{2}+c^{2}+17=2(a-8 b-2 b^{2})

We can write this as,

⇒ \;\; a^{2}-2 a+1+4 b^{2}+16 b+16

+c^{2}=0

⇒(a-1)^{2}+(2 b+4)^{2}+c^{2}=0

⇒ \;\text " Here, we get "\; a=1 \;\text " and "\; 2 b+4=0

⇒ \;\; b=-2

and

c=0

So, value of

(a^{3}+b^{3}+c^{3})

\;\; =1^{3}+(-2)^{3}+0

\;\; =1-8=-7 .

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