Answer:
the three consecutive even integers are -2, 0, 2
Step-by-step explanation:
Let the first even integer = n
Let the second even integer = n + 2
Let the third even integer = n + 4
From the given statement, we form the equation below
(n²) + (n + 2)² + 4 = 2(n + 4)²
Expand this equation;
n² + (n + 2)(n + 2) + 4 = 2(n + 4)(n + 4)
n² + n² + 2n + 2n + 4 + 4 = 2(n² + 4n + 4n + 16)
2n² + 4n + 8 = 2(n² + 8n + 16)
2n² + 4n + 8 = 2n² + 16n + 32
collect like terms together;
2n² - 2n² + 4n - 16n = 32 - 8
- 12n = 24
-n = 24/12
-n = 2
n = -2
Second integer = n + 2
= -2 + 2 = 0
Third integer = n + 4
= -2 + 4
= 2
Therefore, the three consecutive even integers are -2, 0, 2
