SOLUTION: Find three consecutive integers such that the square of the sum of the smaller two is 144 more than the square of the largest.

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: Find three consecutive integers such that the square of the sum of the smaller two is 144 more than the square of the largest.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 189629: Find three consecutive integers such that the square of the sum of the smaller two is 144 more than the square of the largest.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the consecutive integers
a, a%2B1, and a%2B2
The square of the sum of the smaller two is:
%28a+%2B+a+%2B+1%29%5E2
given:
%282a+%2B+1%29%5E2+=+%28a+%2B+2%29%5E2+%2B+144
4a%5E2+%2B+4a+%2B+1+=+a%5E2+%2B+4a+%2B+4+%2B+144
3a%5E2+%2B+4a+%2B+1+=+4a+%2B+148
3a%5E2+=+147
a%5E2+=+49
a+=+7
a%2B1+=+8
a+%2B+2+=+9
The three consecutive integers are 7, 8, and 9
check:
%28a+%2B+a+%2B+1%29%5E2+=+%28a+%2B+2%29%5E2+%2B+144
%287+%2B+8%29%5E2+=+9%5E2+%2B+144
225+=+81+%2B+144
225+=+225
OK