SOLUTION: Hi, Thank you for answering my question in advance. My question is: Find two numbers whose difference is 10 and the sum of whose squares is 250. I set up two formulas f

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi, Thank you for answering my question in advance. My question is: Find two numbers whose difference is 10 and the sum of whose squares is 250. I set up two formulas f      Log On


   

Question 1010951: Hi,
Thank you for answering my question in advance.
My question is:
Find two numbers whose difference is 10 and the sum of whose squares is 250.
I set up two formulas for this question:
1) x-y = 10
2) x^2 + y^2 = 250
I am wondering where I went wrong.
Thank you
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find two numbers whose difference is 10 and the sum of whose squares is 250.
x - y = 10
x = y + 10
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Response to Comment, generally when you are dealing with word problems, you do discard the negative solution.
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:
x^2 + y^2 = 250
replace x with (y+10)
(y+10)^2 + y^2 = 250
FOIL
(y+10)(y+10)
y^2 + 20y + 100 + y^2 = 25
Combine like terms
2y^2 + 20y + 100 - 250 = 0
2y^2 + 20y - 150 = 0
Factors
(2y + 30)(y - 5) = 0
positive solution is what we want here
y = 5
Find x
x = 5 + 10
x = 15
:
:
Check in the 2nd equation
15^2 + 5^2 = 250
225 + 25 = 250