Question 178286

Consecutive even integers are of the form {{{2x}}}, {{{2x+2}}}, {{{2x+4}}}, etc...



So the word problem translates to {{{(2x+4)^2=(2x+2)^2+100}}}



{{{(2x+4)^2=(2x+2)^2+100}}} Start with the given equation.


{{{4x^2+16x+16=4x^2+8x+4+100}}} FOIL


{{{4x^2+16x+16-4x^2-8x-4-100=0}}} Get all terms to the left side.


{{{8x-88=0}}} Combine like terms.


{{{8x=88}}}  Add {{{88}}} to both sides.


{{{x=(88)/(8)}}} Divide both sides by {{{8}}} to isolate {{{x}}}.


{{{x=11}}} Reduce.


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Answer:

So the answer is {{{x=11}}} which means that the numbers are

{{{2(11)=22}}}

{{{2(11)+2=24}}}

{{{2(11)+4=26}}}

So the numbers are 22, 24, and 26