Question

The sum of the squares of two consecutive even numbers is `52`. What are the numbers?

Answer 1

The two consecutive positive even numbers are 4 and 6 respectively.

Explanation:

Even numbers`=0,2,4,6,8...`

Consecutive numbers are numbers that, simply, follows each other.

Let the smaller number`=x^2`, and the larger number be`=(x+2)^2`.

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

Open up the parentheses,

`2x^2+4x+4=52`

Subtract `52` from both sides,

`2x^2+4x-48=0`

Divide both sides by `2`,

`x^2+2x-24=0`

Factorise,

`(x-4)(x+6)=0`
`x=4 or -6` ( reject as `x>0` )

Hence, the two numbers are 4 and 6 respectively.

Answer 2

4 and 6

Explanation:

Let `x` represent one of the integers. Since they are consecutive, even numbers, the other number can be represented as `(x+2)`

Now, we can solve an equation. For this problem, the equation is:

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

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

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

`2x^2+4x+4 = 52`

`x^2+2x+2 = 26`

`x^2+2x+2-26 = 0`

`x^2+2x-24 = 0`

Now you can factor the simple trinomial.

`(x+6)(x-4) = 0`

The values of `x` are: `-6 and 4`

Since `x` cannot be negative, `-6` is extraneous.

Therefore the values of the two integers are 4 and 6.

This works; `4^2 = 16` while `6^2=36`

`36+16 = 52`

Hope this helps!