If x and y are positive real numbers such that `x^(2)y^(3)=32` then the least value of `2x+3y` isA. 5B. 10C. 20D. 15

If x and y are positive real numbers such that `x^(2)y^(3)=32` then th

1.	If x and y are positive real numbers such that `x^(2)y^(3)=32` then the least value of `2x+3y` isA. 5B. 10C. 20D. 15
Answer» Correct Answer - B Let `S=2x+3y.` Then, `S=x+x+y+y+y` Clearly, S is the sum of five terms and the product of these five terms `i.e. x^(2)y^(3)` is given as a constant equal to 32. Therefore, S is least when all these factors are equal `i.e.x=y.` `:." "x^(2)y^(3)=32impliesx^(5)=2^(5)impliesx=2` Hence, the least value of S is given by `S=2xx2+3xx2=10.`

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