If (4x - 7y) = 11 and xy = 8, what is the value of 16x2 + 49y2, given that x and y are positive numbers?

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SSC CGL 2022 Tier-I Official Paper (Held On : 06 Dec 2022 Shift 3)
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  1. 596
  2. 484
  3. 569
  4. 448

Answer (Detailed Solution Below)

Option 3 : 569
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Detailed Solution

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Given:

4x - 7y = 11

xy = 8

Concept used:

(a + b)2 = a2 + b2 + 2ab

Calculation:

4x - 7y = 11

⇒ (4x - 7y)2 = 112

⇒ 16x2 + 49y2 - 56xy = 121

16x2 + 49y2 - 448 = 121

⇒ 16x2 + 49y2 = 121 + 448

16x2 + 49y2 = 569

∴ The required answer is 569.

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