One number is 2 more than another. The difference between their squares is 52. What are the numbers?

Question

I need help finding the smaller and larger numbers trying to find the diffrence of 52

Answer 1

Depending on the level of algebra you are studying, you may be using the word "difference" in two ways:

   1)  the second number minus the first, or

   2)  the absolute value of the distance between the numbers on the number line

 

Let x = one number

    x - 2 = another number

 

Translate:

  "The difference between their squares is 52"   means

      | x² - (x-2)² | = 52

 

So, either:

      x² - x² -4x + 4 = 52

                -4x = 48

                   x = -12

           The numbers are -12 (that is, x) and -14 (that is, x-2)

 or else

    -(x² - x² - 4x + 4) = 52

                  4x - 4 = 52

                  4x = 56

                   x = 14

           The numbers are 14 (that is, x) and 12 (that is, x-2)

             

Answer 2

You have a number lets call it x and another number that is 2 more than x, x+2. Since 52 is the difference between their squares you have,

52=(x+2)²-(x)².

Now solve for x.

And the two numbers are x and x+2.

Answer 3

(x+2)^2-x^2=52

x^2+ 4x +4 -x^2=52

4x+4=52

4x=48

x=12