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SSC CGL 2021 PYQ — Question 66

SSC CGL - 20 Aug 2021 - Shift 1 • Quantitative Aptitude • Q66

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If a2 + b2 + c2 + 216 = 12(a + b - 2c), then ab−bc−ca\sqrt{ab-bc-ca} is:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 65\sqrt{5}

⇒ a2 + b2 + c2 + 216 = 12(a + b - 2c)

⇒ a2 - 12a + b2 - 12b + c2 - 24c + 216 = 0

Now one needs to split 216,

⇒ a2 - 12a + 36 +  b2 - 12b + 36 + c2 + 24c + 144 = 0

⇒ (a - 6)2 + (b - 6)2 + (c + 12)2 = 0.

⇒ a = 6, b = 6 and c = -12

ab−bc−ca\sqrt{ab-bc-ca} = 36+72+72\sqrt{36 + 72 + 72} =  65\sqrt{5}