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

2 Answers
Evan
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.

avo
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!

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