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SSC CHSL 2021 PYQ — Question 52

SSC CHSL - 13 April 2021 - Shift 3 • Quantitative Aptitude • Q52

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If a2 + b2 + c2 = 170 = 2(8a + 5b - 9c), then the value of 4a+8b−c\sqrt{4a+8b-c} will be

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 9

a2 + b2 + 2ab = (a + b)2

a2 + b2 - 2ab = (a - b)2

a2 + b2 + c2 + 170 = 2(8a + 5b - 9c)

a2 + b2 + c2 - 16a - 10b + 18c + 170 = 0 

a2 - 16a + 64 + b2 - 10b + 25 + c2 + 18c + 81 = 0 (∵ 64 + 25 + 81 = 170)

(a - 8)2 + (b - 5)2 + (c + 9)2 = 0

Now,

(a - 8)2 = a - 8 = 0

⇒ a = 8, 

Similarly, the values of b and c are 5 and  -9

Now,

⇒ √(4a + 8b - c) = [(32 + 40 - (- 9)]

⇒ √(72 + 9)
⇒ √81

⇒ 9