Algebra
posted by Tom on .
There are three consecutive integers the square of the largest one equals the sum of the squares of the two other.Find the integers

The numbers are represented by x, x+1 and X+2.
X^2 + (X+1)^2=(X+2)^2
X^2 + X^2 +2X +1=X^2 +4X + 4
2X^2+2X+1=X^2+4X+4
X^22X3=0
(X3)(X+1)=0
X=3 X=1
The numbers are X=3, X+1=4 X+2=5
Check: 3^2 + 4^2=5^2
9+16=25
A second solution is X=1 X=0 X=1
1^2 + 0^2=1^2
1+0=1 
Three consecutive integers (x1), x, (x+1)
(could have said x,x+1,x+2 or x+10,x+11,x+12 etc)
"the square of the largest one equals the sum of the squares of the two other"
> (x+1)^2 = x^2 + (x1)^2
x^2 + 2x + 1 = x^2 + x^2  2x + 1
0 = x^2  4x
x(x4) = 0
x = 0 or x = 4
Case 1: x = 0
The integers are 1, 0, and 1
Case 2: x = 4
The integers are 3,4,and 5
Both solutions work, check them out 
thank so much