Construct a system of nonlinear equations to describe the given behavior, then solve for the requested solutions. Two positive numbers add up to 210. One number is twice the square of the other number. What are the numbers? (Enter your answers as a comma-separated list.)

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Asked Nov 25, 2019
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Construct a system of nonlinear equations to describe the given behavior, then solve for the requested solutions.

Two positive numbers add up to 210. One number is twice the square of the other number. What are the numbers? (Enter your answers as a comma-separated list.)

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Expert Answer

Step 1
Let the two numbers be x and y.
Given that, the two numbers are adding up to 210.
That is equation isx +y 210
-1)
Also given that, one number is twice the square of the other number
2 (2)
That is, the equation is x
2y
help_outline

Image Transcriptionclose

Let the two numbers be x and y. Given that, the two numbers are adding up to 210. That is equation isx +y 210 -1) Also given that, one number is twice the square of the other number 2 (2) That is, the equation is x 2y

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Step 2
Substitute (2) in (1) to find the value ofy
(2y2)+y 210
2y2 210 0
21
= 0
2
(y-10y
21
y10 and y
2
21
Since the given numbers are positive, ignore the root y =
2
help_outline

Image Transcriptionclose

Substitute (2) in (1) to find the value ofy (2y2)+y 210 2y2 210 0 21 = 0 2 (y-10y 21 y10 and y 2 21 Since the given numbers are positive, ignore the root y = 2

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