<PRE><B>Question 243740</B>
Find three consecutive even integers such that the square of the largest exceeds the sum of the squares of the other two by 12.
----------------------
1st: 2x
2nd: 2x+2
3rd: 2x+4
------------------
Equation:
(2x+4)^2 = (2x)^2 + (2x+2)^2 + 12
------------------------------------------
4x^2 + 16x + 16 = 4x^2 + 4x^2 + 8x + 4 + 12
4x^2-8x = 0
4x(x-2) = 0
x = 0 or x = 2
-----------------------
If x = 0
2x = 0
2x+2 = 2
2x+4 = 4
Check:
4^2 = 0^2 + 2^2 + 12
Good solution
-------------------------------
If x = 2
2x = 4
2x+2 = 6
2x+4 = 8
Check:
8^2 = 6^2 + 2^2 + 12
64 = 36 + 16
x=2 does not give a solution set.
===================================
Cheers,
Stan H.</PRE>