1.

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. \(\frac{1}{{62}}(64 + 21\sqrt 5 )\)

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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