SOLUTION: The product of two consecutive positive even integers is 360. Find the integers.

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Question 113275: The product of two consecutive positive even integers is 360. Find the integers.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Consecutive even integers follow the form: 2x, 2x%2B2, etc


So when they say "The product of two consecutive positive even integers is 360", they mean symbolically:

%282x%29%282x%2B2%29=360


4x%5E2%2B4x=360 Distribute


4x%5E2%2B4x-360=0 Subtract 360 from both sides


4%28x%5E2%2Bx-90%29=0 Factor 4x%5E2%2B4x-360



4%28x%2B10%29%28x-9%29=0 Factor x%5E2%2Bx-90 (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:

x%2B10=0 or x-9=0

x=-10 or x=9 Now solve for x in each case


So our solutions are x=-10 or x=9


However, since it is stated that the integers must be positive, x=9 is the only solution


Now plug x=9 into 2x to find the 1st number:

2%289%29=18

So our 1st number is 18




Now plug x=9 into 2x%2B2 to find the 2nd number:

2%289%29%2B2=18%2B2=20

So our 2nd number is 20



So our two numbers are 18 and 20


Check:

When we multiply 18 and 20, we should get 360

18%2A20=360


360=360 Since we do, our answer is verified.