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SSC CHSL 2019 PYQ — Question 55

SSC CHSL - 11th July 2019 - Shift 1 • Quantitative Aptitude • Q55

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If (3x + 1)3 + (x – 3)3 + (4 – 2x)3 + 6(3x + 1) (x – 3) (x – 2) = 0, then x is equal to:

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Correct answer: B

Explanation

The Correct Answer is option 2 i.e. -1

Concept
If a3 + b3 + c3 = 3abc, then a + b + c = 0

Application

(3x + 1)3 + (x – 3)3 + (4 – 2x)3 + 6(3x + 1) (x – 3) (x – 2) = 0

It can be written as:

(3x + 1)3 + (x – 3)3 + (4 – 2x)3 – 3(3x + 1) (x – 3) (4 – 2x) = 0

We know, If a3 + b3 + c3 = 3abc, then a + b + c = 0

Hence,

(3x + 1) + (x – 3) + (4 – 2x) = 0

⇒ 2x + 2 = 0

⇒ 2x = -2

⇒ x = -1