minimum value of 4a^2+9b^2+12a-24b+25 Detail solution for this type..

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5 distinct balls and 3 distinct boxes are given. Find the no. of ways such that no box contain more than 1 ball

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What will be the solution to this question? The answer is 10.

Minimum value 0.

Write 4a^2 + 12a in form of perfect square, it will be written as 4(a^2 +9/4 + 2*3a/2), do the same thing for the elements containing b too, you shall have this: 4(a+3/2)^2 + 9(b-4/3)^2.