The sum of the squares of two consecutive even numbers is 5252. What are the numbers?

2 Answers
Dec 4, 2017

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.

Dec 4, 2017

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!