Question

Find two consecutive possitive even integers the sum of whose square is 164

Answer 1

8 and 10.

Explanation:

Let the integers be x and x+2, then:

x^2 + (x+2)^2 = 164

x^2 + x^2 + 4x + 4 - 164 = 0

2x^2 + 4x - 160 = 0

2(x^2 + 2x - 80) = 0

2(x + 10)(x - 8) = 0

x = -10, 8

We ignore the negative root, so:

The numbers are 8 and 8 + 2

= 8 and 10.