यदि x = 4 + √6 और y = 4 - √6 है, तो x² + y² का मान क्या है?

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SSC CGL 2024 Tier-II Official Paper-I (Held On: 20 Jan, 2025)
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  1. 51
  2. 42
  3. 44
  4. 43

Answer (Detailed Solution Below)

Option 3 : 44
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दिया गया है:

यदि x = 4 + √6 और y = 4 - √6

प्रयुक्त सूत्र:

x² + y² = (x + y)² - 2xy

गणना:

x = 4 + √6 और y = 4 - √6

x + y = (4 + √6) + (4 - √6) = 8

x × y = (4 + √6)(4 - √6) = 4² - (√6)² = 16 - 6 = 10

इसलिए, x² + y² = (8)² - 2 × 10

इसलिए, x² + y² = 64 - 20

इसलिए, x² + y² = 44

इसलिए, सही उत्तर विकल्प (3) है।

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