SOLUTION: Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 80789: Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
"Three consecutive even integers"
x, (x+2), (x+4)
:
"are such that the square of the third is 76 more than the square of the second."
(x+4)^2 = (x+2)^2 + 76
:
x^2 + 8x + 16 = (x^2 + 4x + 4) + 76
:
x^2 + 8x + 16 = x^2 + 4x + 80
:
x^2 - x^2 + 8x - 4x = 80 - 16
:
4x = 64
:
x = 16
:
16, 18, 20 are the numbers
:
:
Check on calc: 20^2 - 18^2 = 76