The sum of the squares of two consecutive positive even integers is 340. How do you find the number?

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Answer 1 · 2018-04-10T05:25:41

The numbers are #12# and #14#

To find the answer, set up an equation.

Set #x# equal to the lower number, and #x+2# as the higher number since they are consecutive even numbers so they are two apart.

Now write out the equation according to the question

#(x)^2+color(blue)((x+2))^2 = 340#

#x^2 + color(blue)(x^2 + 4x + 4) = 340#

Combine like terms.

#2x^2 + 4x + 4 = 340#

Set equal to zero so you can factor.

#2x^2 + 4x -336 = 0#

#(2x+ 28)(x-12) = 0#

#x= -14, 12#

#x=12# because the answer must be positive according to the question.

That means #x+2# is 14.

You can double check:

#(12)^2 + (14)^2= 340#

#144+196=340#

#340=340#