Question 733158
If n is the first of two consecutive even integers,
 write an equation that can be used to find the integers
 if the sum of the squares of twice the first and the second is 100.
:
let n and (n+2) = the two even consecutive integers
:
the sum of the squares of twice the first and the second is 1
(2x)^2 + (x+2)^2 = 100
4x^2 + x^2 + 4x + 4 = 100
5x^2 + 4x + 4 - 100 = 0
5x^2 + 4x - 96 = 0
Factors to
(5x+24)(x-4) = 0
the integer solution
x = 4
:
The two consecutive even integers: 4, 6
:
:
Check 8^2 + 6^2 = 100