Answer:
The numbers are #12# and #14#
Explanation:
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#
Note:
Here you go I hope this helps
