SOLUTION: The product of three consecutive integers is twenty-six thousand nine hundred seventy.

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Question 1203672: The product of three consecutive integers is twenty-six thousand nine hundred seventy.
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
You'd probably start with x being the smallest integer:

x%28x%2B1%29%28x%2B2%29=26970

I'd start with x being the middle one of the three: 

%28x-1%29%28x%29%28x%2B1%29=26970

because it would be easy to multiply out (x-1)(x+1)

But heck! x is bound to be near the cube root of 26970,
So pick up a calculator that can take cube roots:

root%283%2C26970%29%22%22=%22%22%2229.98888477...%22

That's close to 30, so try 30 as the middle one

Try 29,30,31  

29%2A30%2A31%22%22=%22%2226970  <--That's it!

That's a quick way to get the answer, and since factoring 
and solving a cubic equation requires trial and error with 
synthetic division anyway, I'd say the above way is the 
best way to do it.  Other tutors might disagree.

Answer: 29,30,31

Edwin

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The product of three consecutive integers is very nearly equal to the cube of the middle one.

Since 27000 is 30^3, the numbers are almost certainly 29, 30, and 31.

Multiplying those three consecutive integers gives the correct result 26970....

ANSWERS: 29, 30, and 31