SSC CGL 23 Aug 2021 Shift 1 Paper

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Question : 51 of 100

Marks: +1, -0

If

8+2 p x^{2}-36 x-27 x^{3}=(2-3 x)^{3}

, then what is the value of

p

?

27
9
$-27$
54

Solution:

Given,

8+2 p x^{2}-36 x-27 x^{3}=(2-3 x)^{3}

We know that,

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

⇒(2-3 x)^{3} \;\; =(2)^{3}-(3 x)^{3}

\;\; -3 × 2 × 3 x(2-3 x)

\;\; =8-27 x^{3}-36 x+54 x^{2}

\;\text " Compare with "\; 8-27 x^{3}-36 x+2 p x^{2}

\;\text " We get, "\; 54 x^{2}=2 p x^{2}

⇒ \;\; 2 p=54

⇒ \;\; p=27

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