Algebra
posted 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

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
Respond to this Question
Similar Questions

math, algebra
2a+2ab+2b I need a lot of help in this one. it says find two consecutive positive integers such that the sum of their square is 85. how would i do this one i have no clue i know what are positive integers.but i don't know how to figure … 
math
Consecutive integers are integers that follow each other in order (for example 5, 6, and 7). The sum of three consecutive integers is 417.Let n be the first one. Write an equation that will determine the three integers. 
Algebra
The sum of the squares of the largest and smallest of three consecutive odd integers is 353 less than 3 times the square of the middle one. Find the integers. 
Algebra
The sum of the squares of two consecutive positive even integers is one hundred sixtyfour. Find the two integers. 
Algebra
The difference of the cubes of two consecutive odd positive integers is 400 more than the sum of their squares. Find the sum of the two integers. 
math
A. Four times one odd integer is 14 less than three times the next even integer. Find the integers. B. The average of four consecutive odd integers is 16. Find the largest integer. C. When the sum of three consecutive integers is divided … 
Math
find three consecutive positive odd integers such that the sum of the squares of the first and second integers is equal to the square of the third integer minus 7? 
math
What is the smallest of three consecutive integers if the sum of the smaller two integers is equal to 177 less than four times the largest? 
math
What is the smallest of three consecutive integers if the sum of the smaller two integers is equal to 177 less than four times the largest? 
math
What is the smallest of three consecutive integers if the sum of the smaller two integers is equal to 177 less than four times the largest?