Question 293336: two numbers add to 17 and the sum of their squares is 185. what are the two numbers?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! two numbers add to 17
x + y = 17
y = (17-x)
:
the sum of their squares is 185.
x^2 + y^2 = 185
:
what are the two numbers?
Replace y with (17-x), find x
x^2 + (17-x)^2 = 185
FOIL
x^2 + (289 - 34x + x^2) = 185
:
x^2 + x^2 - 34x + 289 - 185 = 0
:
2x^2 - 34x + 104 = 0
factors to
(2x - 8)(x - 13) = 0
Two solutions, giving us the two numbers
x = 13
and
2x = 8
x = 4
:
Check solutions: 13^2 + 4^2 = 185
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