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?

Printable View

- Apr 18th 2011, 01:21 AMpranayFinding 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? - Apr 18th 2011, 01:43 AMearboth
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. - Apr 18th 2011, 01:46 AMveileen
http://img23.imageshack.us/img23/989...f672c78a0c.png

http://img822.imageshack.us/img822/3...45e34896d6.png and http://img155.imageshack.us/img155/5...8747f2b9ab.png

So http://img705.imageshack.us/img705/4...87c6869355.png, S is minumum http://img52.imageshack.us/img52/710...5be4a33aad.png and http://img694.imageshack.us/img694/3...b752591367.pnghttp://img847.imageshack.us/img847/2...6db0ae6460.png