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If a : b = 3 : √5, then the value of (2a + b) : (3a - 2b) is:1. \(\frac{1}{{61}}(64 + 21\sqrt 5 )\)2. \(\frac{1}{{64}}(64 + 21\sqrt 5 )\)3. \(\frac{1}{{63}}(64 + 21\sqrt 5 )\)4. \(\frac{1}{{62}}(64 + 21\sqrt 5 )\) |
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Answer» Correct Answer - Option 1 : \(\frac{1}{{61}}(64 + 21\sqrt 5 )\) Given: a ∶ b = 3 ∶ √5 Calculation: Let a, b be 3k, k√5 ⇒ 2a + b = 6k + k√5 ⇒ 3a – 2b = 9k – 2k√5 (2a + b) ∶ (3a – 2b) ⇒ (6k + k√5) ∶ (9k – 2k√5) ⇒ (6 + √5)(9 + 2√5) ∶ (92 – (2√5)2) ⇒ (64 + 21√5)/61 ∴ (2a + b) ∶ (3a – 2b) is (64 + 21√5)/61 |
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