InterviewSolution
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InterviewSolution
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What is the minimum value of `a^(2)x+b^(2)y` where `xy=c^(2)` ?A. abcB. 2abcC. 3abcD. 4abc |
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Answer» 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`. |
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