Question

The square of the sum of two consecutive positive even integers is 4048 more than the sum of the squares of these two numbers. Find the two numbers.

Answer 1

The numbers are 44 and 46

Explanation:

Let

x, x+2 ----> the two consecutive positive even integers

we know that

`(x+x+2)^(2) =4,048+x^(2) +(x+2)^(2) \\ \\(2x+2)^(2) =4,048+x^(2) +x^(2)+4x+4\\ \\4x^(2)+8x+4=2x^(2)+4x+4,052\\ \\2x^(2) +4x-4,048=0`

Solve the quadratic equation using a graphing calculator

The solution is x=44

see the attached figure

`x+2=44+2=46`

therefore

The numbers are 44 and 46