# Algebra

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There are three consecutive integers the square of the largest one equals the sum of the squares of the two other.Find the integers

• Algebra -

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^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 -

Three 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 -

thank so much

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