Find three consecutive even intergers such that the square of the sum of the first and second intergers is equal to twice the third interger

Question

Help on solving word equation set up to solve

Answer 1

I will set this up for you, and you can do the math.

 

Let the 3 consecutive even integers be n, n + 2, and n + 4.  Then the problem statement translates into

 

[n + (n + 2)]² = 2(n + 4)

 

Expand this and simplify it, and you will get a quadratic equation in n.  Solve for n, then get n + 2 and n + 4.  (Note:  The quadratic equation may give 2 values for n, so you may end up with 2 sets of 3 integers that satisfy the problem conditions.)

 

Can you take it from here?