SOLUTION: Among all pairs of numbers (x,y) such that 4x+2y=24, find the pair for which the sum of squares, x2+y2, is minimum. Write your answers as fractions reduced to lowest terms.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Among all pairs of numbers (x,y) such that 4x+2y=24, find the pair for which the sum of squares, x2+y2, is minimum. Write your answers as fractions reduced to lowest terms.      Log On


   

Question 1146085: Among all pairs of numbers (x,y) such that 4x+2y=24, find the pair for which the sum of squares, x2+y2, is minimum. Write your answers as fractions reduced to lowest terms.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Solve the linear equation for one of the variables.

4x%2B2y+=+24
2x%2By+=+12
y+=+12-2x

Substitute

x%5E2%2By%5E2+=+x%5E2%2B%2812-2x%29%5E2+=+5x%5E2-48x%2B144

The minimum value of a quadratic function is when x = -b/2a = 48/10 = 24/5.

y+=+12-2x+=+12-48%2F5+=+12%2F5

ANSWERS: x = 24/5; y = 12/5