If X + Y = 23 and XY = 126; what is the value of (X)² + (Y)² = ?

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CSIR-CLRI JSA 2024 Official Paper-I (Held On: 16 Feb, 2025)
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  1. 250
  2. 277
  3. 340
  4. 386

Answer (Detailed Solution Below)

Option 2 : 277
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Detailed Solution

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Given:

X + Y = 23

XY = 126

Formula used:

(X + Y)2 = X2 + Y2 + 2XY

Calculation:

232 = X2 + Y2 + 2 × 126

⇒ 529 = X2 + Y2 + 252

⇒ X2 + Y2 = 529 - 252

⇒ X2 + Y2 = 277

∴ The correct answer is option (2).

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