SOLUTION: find two numbers such that one number is 5 greater than the other number. If the sum of their squares is 5 times the square of half the smaller number, what are the numbers?

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Question 1087714: find two numbers such that one number is 5 greater than the other number. If the sum of their squares is 5 times the square of half the smaller number, what are the numbers?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
find two numbers; a & b
such that one number is 5 greater than the other number.
a = b + 5
If the sum of their squares is 5 times the square of half the smaller number,
a^2 + b^2 = 5(.5b)^2
:
what are the numbers?
Replace a with (b+5) in the above equation
(b+5)^2 = 5(.5b)^2
b^2 + 10b + 25 + b^2 = 5*.25b^2
2b^2 + 10b + 25 = 1.25b^2
2b^2 - 1.25b^2 + 10b + 25 = 0
.75b^2 + 10b + 25 = 0
I got an integer solution
b = -10
then
a = -10 + 5
a = -5
:
The two numbers are -5 and -10
:
;
See if that checks out
-5^2 + -10^2 = 5(.5(-10))^2
25 + 100 = 5(.25(100))
125 = 5(25)