The difference between the square of one even number and the square of the next smaller even number is 52.?

Question

What is the larger number?
10

14

17

Answer 1

Let n ne the larger, so that the smaller is n-2. We have n^2 - (n-2)^2 = 2(2n -2) = 52 => 2n -2 = 26 => n = 28/2 = 14, actually an even number.

So, the number is 14.

Answer 2

All even numbers are in the form of 2n, where n is some integer. The even number that comes before this is 2n - 2. So the square of the larger one minus the square of the smaller one is (2n)^2 - (2n-2)^2 = 52. This is:
4n^2 - 4(n-1)^2 = 52
n^2 - (n-1)^2 = 13
n^2 - (n^2 - 2n + 1) = 13
2n - 1 = 13
2n = 14
We said 2n was the larger number, so the answer is 14.

Answer 3

eliminate 17 (not an even number)
try 10: 10x10 - 8x8 = 100-64 = 36
must be 14
14x14 - 12x12 = 196 - 144 = 52

Answer 4

let x be the first number.
x - 2 is the next small even number

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

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

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

4x - 4 = 52

4x = 56

x = 14


the larger number is 14

Answer 5

14 (196-144=52)

Answer 6

Let even no. be 2x
Next smaller even no. is 2x - 2
(2x)² - (2x - 2)² = 52
4x² - (4x² - 8x + 4) = 52
8x - 4 = 52
8x = 56
x = 7
Larger even no. is 14