SOLUTION: Among all pairs of numbers (x,y) such that 2x+y=16, 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 -> SOLUTION: Among all pairs of numbers (x,y) such that 2x+y=16, 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 1115200: Among all pairs of numbers (x,y) such that 2x+y=16, find the pair for which the sum of squares, x2+y2, is minimum. Write your answers as fractions reduced to lowest terms.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2By%5E2
x%5E2%2B%2816-2x%29%5E2
x%5E2%2B%2816%5E2-64x%2B4x%5E2%29
5x%5E2-64x%2B16%5E2
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%28d%2Fdx%29%285x%5E2-64x%2B16%5E2%29
10x-64

Let expression for derivative be 0.
10x-64=0
10x=64
x=64%2F10
x=32%2F5=6%262%2F5
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y=16-2x
y=16-2%2832%2F5%29
y=16-64%2F5
y=3%261%2F5
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The two numbers x and y
( 6&2/5, 3&1/5 )