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January 24, 2017
Posted by **Tom** on Wednesday, March 24, 2010 at 8:46pm.

- Algebra -
**Kathleen**, Wednesday, March 24, 2010 at 8:59pmThe 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^2-2X-3=0

(X-3)(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 - Algebra -
**Reiny**, Wednesday, March 24, 2010 at 9:01pmThree consecutive integers (x-1), 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 + (x-1)^2

x^2 + 2x + 1 = x^2 + x^2 - 2x + 1

0 = x^2 - 4x

x(x-4) = 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 - Algebra -
**Tom**, Wednesday, March 24, 2010 at 9:11pmthank so much