SOLUTION: One number is 5 greater than another number. If The sum of their squares is 5 times the square of the smaller number, what are the numbers?

Question 119280: One number is 5 greater than another number. If The sum of their squares is 5 times the square of the smaller number, what are the numbers?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
One number is 5 greater than another number. If The sum of their squares is 5 times the square of the smaller number, what are the numbers?
:
Let x = "One number"
then
(x-5) = "another number"; (assume it is the smaller number)
:
"If The sum of their squares is 5 times the square of the smaller number,"
x^2 + (x-5)^2 = 5(x-5)^2
:
Subtract (x-5)^2 from both sides:
x^2 = 5(x-5)^2 - (x-5)^2
:
x^2 = 4(x-5)^2
:
x^2 = 4(x^2-10x+25)
:
x^2 = 4x^2 - 40x + 100
:
3x^2 - 40x + 100 = 0; subtracted x^2 from both sides
:
Factor this to:
(3x - 10)(x - 10) = 0
:
x =
and
x = 10; the integer solution is what we want here.
:
"what are the numbers?"
:
numbers are 10 and 5
:
:
Check solution using the statement:
"If The sum of their squares is 5 times the square of the smaller number,
10^2 + 5^2 = 5(5^2)
100 + 25 = 5(25); confirms our solution
:
Note the other solution x = 10/3 may also be a valid answer since they did not specify that they had to be integers. Check that out.

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