SOLUTION: here is the problem : One number is 2 greater than another number.If the sum of their squares is 5 times the square of the smaller number,what are the numbers?

Question 235404: here is the problem : One number is 2 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!
Let x = "one number"
Let y = "another number"
:
Write an equation for each statement:
:
"One number is 2 greater than another number."
x = y + 2
:
"the sum of their squares is 5 times the square of the smaller number,"
x^2 + y^2 = 5y^2
x^2 = 5y^2 - y^2
x^2 = 4y^2
:
What are the numbers?
From the 1st statement we know x = (y+2)
replace x with (y+2)
(y+2)^2 = 4y^2
FOIL
y^2 + 4x + 4 = 4y^2
Arrange as a quadratic on the right
0 = 4y^2 - y^2 - 4x - 4
0 = 3y^2 - 4y - 4
Factor this to
(3y + 2)(y - 2) = 0
Two solutions
3y = -2
y =
and
y = 2
:
Find x when y = -2/3
x = + 2
x =
:
Find x when y = 2
x = 2 + 2
x = 4
:
x = 4, y = 2 and x = 4/3, y = -2/3
:
You should check both solutions in: x^2 + y^2 = 5y^2
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