SOLUTION: Find two integers whose sum is 12 and whose squares differ by 24. Here's what I tried. x + y = 12 , x^2 - y^2 = 24 x = -y + 12 (-y + 12)^2 - y^2 = 24 y^2 - 24y + 24 - y^2 =

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Find two integers whose sum is 12 and whose squares differ by 24. Here's what I tried. x + y = 12 , x^2 - y^2 = 24 x = -y + 12 (-y + 12)^2 - y^2 = 24 y^2 - 24y + 24 - y^2 =       Log On


   

Question 427847: Find two integers whose sum is 12 and whose squares differ by 24.
Here's what I tried.
x + y = 12 , x^2 - y^2 = 24
x = -y + 12
(-y + 12)^2 - y^2 = 24
y^2 - 24y + 24 - y^2 = 24
-24y + 24 = 24
-24y = 0
y = 0
x + 0 = 12
x = 12
But then it won't match the other problem?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The error in your solution is on the fourth line: When you expand %28-y+%2B+12%29%5E2 you should get y%5E2+-+24y+%2B+144, not y%5E2+-+24y+%2B+24.

From this, we get
y%5E2+-+24y+%2B+144+-+y%5E2+=+24
-24y+%2B+144+=+24
-24y+=+-120 --> y = 5, x = 7. Also, 7^2 - 5^2 = 24.