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.

PLZZZZZ I NEED LE HELP FROM LE FELLOW STUDENTS!!!

Answer 1

44 and 46

Explanation:

Let

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

we know that

`(x+x+2)^(2)=x^(2)+(x+2)^(2) +4,048`

Solve for x

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

Solve the quadratic equation by graphing

The solution is x=44

see the attached figure

therefore

the numbers are

x=44

x+2=46