SOLUTION: The sum of two numbers is 210. If one number is the square of the other, find the set of numbers.

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Question 914732: The sum of two numbers is 210. If one number is the square of the other, find the set of numbers.
Found 2 solutions by ankor@dixie-net.com, jim_thompson5910:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The sum of two numbers is 210.
If one number is the square of the other, find the set of numbers.
:
x^2 + x = 210
x^2 + x - 210 = 0; a quadratic equation
Factors to
(x-14)(x+15) = 0
the positive solution
x = 14, x^2 = 196; 196 + 14 = 210
:
x = -15 also works
-15^2 = +225 - 15 = 210

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
y = x^2

x+y = 210

x+x^2 = 210

x^2 + x - 210 = 0

(x+15)(x-14) = 0

x+15 = 0 or x-14 = 0

x = -15 or x = 14

If you only consider the positive numbers, then ignore x = -15

x = 14

y = x^2

y = 14^2

y = 196

Notice how 14 + 196 = 210. So that confirms the answer.

So the two numbers are 14 and 196

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Thanks,

Jim