Thread: 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?

Originally Posted by pranay

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.

and

So , S is minumum and