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Math Help - Finding the values of a and b

  1. #1
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    Finding the values of a and b

    if i have an expression like:
    S=14a*a+3b*b+6b+12a+3
    then is it possible to find the value of a and b for S to be minimum?
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  2. #2
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    Quote Originally Posted by pranay View Post
    if i have an expression like:
    S=14a*a+3b*b+6b+12a+3
    then is it possible to find the value of a and b for S to be minimum?
    1. I read your equation as: S = 14a^2+3b^2+12a+6b+3

    2. If this is correct, then complete the squares at the RHS:

    S = 14a^2+3b^2+12a+6b+3 ===> S = 14(a+3/7 )^2+3(b+1)^2-18/7

    3. The smallest value of a square is zero. Therefore the smallest value of s occurs if both squares have the value zero. Determine a, b and s.
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  3. #3
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    and

    So , S is minumum and
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