Question 596352: Twice the first number is increased by the second number is 16. Find the two numbers if the sum of their squares is a minimum.
Pleassse help Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! Twice the first number is increased by the second number is 16. Find the two numbers if the sum of their squares is a minimum.
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2x + y = 16
x^2 + y^2 = s
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y = 16 - 2x
x^2 + (16-2x)^2 = s
x^2 + 4x^2 - 64x + 256 = s
5x^2 - 64x + 256 = s
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That's a parabola. Since the coefficient of the x^2 term is +, it opens upward and has a minumum. The minimum is the vertex.
The vertex is on the LOS (Line of Symmetry).
The equation for the line of symmetry is x = -b/2a
x = 64/10 = 6.4
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2x + y = 16
--> y = 3.2
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The answer is 6.4 & 3.2
