Question

What is the minimum value of `a^(2)x+b^(2)y` where `xy=c^(2)` ?
A. abc
B. 2abc
C. 3abc
D. 4abc

Answer 1

Correct Answer - B
Let `p=a^(2)x+b^(2)y` and `xy=c^(2)`
`implies y=c^(2)/x` ...(1)
`implies P=a^(2) x+b^(2) (c^(2)/x)`
Now, `(dp)/(dx)=0implies a^(2)- (b^(2) c^(2))/x^(2)=0`
`:. Y=c^(2)/((bc)/a)=(ac^(2))/(bc)=(ac)/b`
`implies a^(2)=(b^(2)c^(2))/x^(2)`
`implies x=(bc)/a :. P_("min")=a^(2)((bc)/a)+b^(2) ((ac)/b)`
`=abc+abc=2abc`.