(5z - 7y)² + (7z + 5y)² - 49z² को सरल कीजिए

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SSC CGL 2024 Tier-II Official Paper-I (Held On: 20 Jan, 2025)
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  1. 30z² + 83y²
  2. 35z² + 70y²
  3. 26z² + 82y²
  4. 25z² + 74y²

Answer (Detailed Solution Below)

Option 4 : 25z² + 74y²
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दिया गया है:

(5z - 7y)² + (7z + 5y)² - 49z² को सरल कीजिए

प्रयुक्त सूत्र:

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

गणना:

(5z - 7y)2 + (7z + 5y)2 - 49z2

⇒ (25z2 - 2 × 5z × 7y + 49y2) + (49z2 + 2 × 7z × 5y + 25y2) - 49z2

⇒ 25z2 - 70zy + 49y2 + 49z2 + 70zy + 25y2 - 49z2

⇒ 25z2 + 49z2 - 49z2 + 49y2 + 25y2

⇒ 25z2 + 74y2

इसलिए, सही उत्तर विकल्प (4) है।

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