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SSC CHSL 2023 PYQ — Question 72

SSC CHSL 2023 - 03 Aug 2023 - Shift 4 • Quantitative Aptitude • Q72

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If x3 = 270 + y3 and x = (6 + y), then what is the value of (x + y)? (given that x > 0 and y > 0)

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 434\sqrt3.

x3 = 270 + y3

⇒ x3 -  y3 = 270...................1

x = (6 + y)

⇒ x - y = 6......................2

We know that 

(x - y)3 = x3 - y3 - 3xy(x - y)

So, 

⇒ 63 =  270 - 3xy(6)

⇒ 216 - 270 = -18xy

⇒ xy = 54/18 = 3

(x + y)2 = (x - y)2 + 4xy

⇒ (x + y)2 = (6)2 + 4 × 3

⇒ (x + y)2 = 48

⇒ (x + y) = 434\sqrt3