The difference between the square of one even number and the square of the next smaller even number is 52. What is the larger even number? Is it x-x^2=52 am I in the right track?

Question

anonymous · Answer

no, the way to approach this problem is to set x = a number (odd/even doesnt matter)
we know for sure, 2x = an even number
so now we have the problem
(2x)^2 - (2x-2)^2 = 52
solve for x, then plug back into 2x and 2x-2 for the even numbers, hope this helped!

hero · Answer

x^2 - (x - 2)^2 = 52

You don't need to use 2x to solve this

hero · Answer

x^2 - ((x-2)(x-2)) = 52
    x^2 -(x(x-2)-2(x-2)) = 52
x^2 -(x^2 -2x -2x + 4) = 52
       x^2 - x^2 +4x - 4 = 52
                         0 + 4x = 52 + 4
                               4x = 56
                                 x = 14
                           x - 2 = 12

14^2 - (14 - 2)^2 = 52
    14^2 - (12)^2  = 52
       14^2 - 12^2 = 52
           196 - 144 = 52
                      52 = 52

Therefore the consecutive numbers are 14 and 12

anonymous · Answer

@Hero thank so much for helping me out!