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SSC CGL 2022 PYQ — Question 67

SSC CGL - 21 April 2022 - Shift 2 • Quantitative Aptitude • Q67

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If a2 + b2 = 65 and ab = 8, a > b > 0, then find the value of a2 - b2.

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 63.

a2 + b2 = 65 and ab = 8

(a + b)2 = a2 + b2 + 2ab

(a - b)2 = a2 + b2 - 2ab

⇒ a2 - b2 = (a + b)(a - b)

⇒ a2 + b2 + 2ab = 65 + 16

⇒ (a + b)2 = 81

⇒ (a + b) = 9

Again,

⇒ a2 + b2 - 2ab = 65 - 16

⇒ (a - b)2 = 49

⇒ (a - b) = 7

⇒ a2 - b2 = 9 × 7 = 63