SSC CGL 23 Aug 2021 Shift 2 Paper

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Question : 61 of 100

Marks: +1, -0

If

(x+6)^{3}+(2 x+3)^{3}+(3 x+5)^{3}

=(3 x+18)(2 x+3)(3 x+5)

, then what is the value of

x

?

$-\;{5}/{3}$
$\;{5}/{3}$
$-\;{7}/{3}$
$\;{7}/{3}$

Solution:

(x+6)^{3}+(2 x+3)^{3}+(3 x+5)^{3}

=(3 x+18)(2 x+3)(3 x+5)

We know that

a^{3}+b^{3}+c^{3}=3 a b c

Then,

a+b+c=0

⇒ \;\; (x+6)+(2 x+3)+(3 x+5)=0

⇒ \;\; 6 x+14=0

⇒ \;\; 6 x=-14

⇒ \;\; x=-\;{14}/{6}=-\;{7}/{3}

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