Asked by Tom

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

Answers

Answered by Kathleen
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


Answered by Reiny
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
Answered by Tom
thank so much

Related Questions