Looking at the problem, you can come up with an equation for the consecutive numbers.
[tex] x^{2} + (x + 2)^{2} = 340[/tex]
If we expand the second term:
[tex] x^{2} + x^{2} + 4x + 4 = 340[/tex]
Combine like terms:
[tex]2 x^{2} + 4x + 4 = 340[/tex]
You can reduce this by dividing both sides of the equation by two:
[tex] x^{2} + 2x + 2 = 170[/tex]
And we transpose 170 to get a standard quadratic form that the right side will be zero:
[tex] x^{2} + 2x - 168 = 0[/tex]
Then factor the left side:
[tex](x +14)(x-12) = 0[/tex]
Find out the values of x that makes each factor = 0
x + 14 = 0
x = -14
We can eliminate the negative symbol because the problem is asking for positive even integers.
and;
x - 12 = 0
x = 12
Now we can say that the first positive integer is 12 and the second one is 14
