If x2y3 = 32, find the least possible value of 2x + 3y. (x, y > 0)
Explanation:
In such cases we divided the coefficient of the variable with corresponding power and write the sum in following way.
2x +3y = x + x + y + y + y
Now we have five terms, x, x, y, y and y.
We know, AM ≥ GM [equality occurs when the numbers are equal]
⇒ x+x+y+y+y5 ≥ x×x×y×y×y5
⇒ 2x + 3y ≥ 5 × x2×y35
⇒ 2x + 3y ≥ 5 × 325
⇒ 2x + 3y ≥ 10
∴ Least possible value of (2x + 3y) is 10. [This happen when x = x = y = y = y = 2]
Hence, option (c).
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