Question 159567
Remember consecutive even integers follow the pattern {{{x}}}, {{{x+2}}}, {{{x+4}}}, etc.


Since "product of two consecutive even positive integers is one hundred twenty", this means that  {{{x(x+2)=120}}}


{{{x(x+2)=120}}} Start with the given equation



{{{x^2+2x=120}}} Distribute



{{{x^2+2x-120=0}}} Subtract 120 from both sides



{{{(x+12)(x-10)=0}}} Factor



{{{x+12=0}}} or {{{x-10=0}}} Set each factor equal to zero



{{{x=-12}}} or {{{x=10}}} Solve for "x" in each case.



So the two numbers are 10 and 12 (since we're only looking for positive integers)