If x and y are positive real numbers and x3y2 = 48, then the minimum value of 2x + 3y is?
Explanation:
Given, x3y2 = 24
We need to calculate minimum value of A = 2x + 3y
Since the power of x is 3 and y is 2 in x3y2 = 24, we rewrite write A as 2x3+ 2x3+ 2x3+ 3y2 + 3y2
We know, AM ≥ GM
⇒ 2x3+2x3+2x3+3y2+3y25 ≥ 2x3×2x3×2x3×3y2×3y25
⇒ 2x + 3y ≥ 5 × 23×x3y25
⇒ 2x + 3y ≥ 5 × 23×485
⇒ 2x + 3y ≥ 5 × 325
⇒ 2x + 3y ≥ 10
∴ The least possible value of 2x + 3y = 10
Hence, option (a).
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