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Let x , y > 0 . If x 3 y 2 = 2 15 , then the least value of 3 x + 2 y is

Options

  1. A30
  2. B32
  3. C36
  4. D40

Correct answer

D. 40

Step-by-step solution

Using A . M ≥ G . M , we get x + x + x + y + y 5 ≥ x 3 · y 2 5 ⇒    3 x + 2 y 5 ≥ x 3 y 2 5 ⇒    3 x + 2 y 5 ≥ 2 15 5             ∵       x 3 y 2 = 2 15 ⇒    3 x + 2 y ≥ 5 · 2 15 / 5 ⇒    3 x + 2 y ⩾ 5 × 2 3 ⇒    3 x + 2 y ⩾ 40 ∴ The minimum value of 3 x + 2 y is 40

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