Sum of squares

Question

The sum of the squares of two consecutive positive even integers is 244. Find the numbers

Answer 1

Let the 1st integer = x

Let the 2nd integer = x + 2

 

Using these variables, we can write the equation to show the sum.

 

x² + (x + 2)² = 244

 

 

Solve for x.

 

x² + (x + 2)(x + 2) = 244

 

x² + x² + 4x + 4 = 244

 

2x² + 4x + 4 = 244

 

 

Subtract 244 on both sides of the equation.

 

2x² + 4x - 240 = 0

 

 

Factor out a 2.

 

2(x² + 2x - 120) = 0

 

 

Set the term in parenthesis equal to zero.

 

x² + 2x - 120 = 0

 

 

Factor using FOIL.

 

(x + 12)(x - 10) = 0

 

 

x = -12         and        x = 10

 

 

Since we want positive integers, we accept   x=10.

 

 

So the two integers are 10 and 12.

 

 

To check, we take their squares and add them.  The sum should be 244.

 

10² + 12² = 244

 

100 + 144 = 244

 

          244 = 244

 

 

This checks out!!