SOLUTION: how do you find three consecutive numbers who's product is 15, 600?

Question 149452: how do you find three consecutive numbers who's product is 15, 600?
Found 2 solutions by Alan3354, checkley77:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
how do you find three consecutive numbers who's product is 15,600?
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I'll assume you mean integers.
So, n*(n+1)*(n+2) = 15600
Find the cube root of 15600, = 24.99...
Since the numbers differ by only 1, they'll be approximately 25.
Try 24*25*26, which is 15600.
I doubt the instructor will accept the method, but it's the right answer.
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
LET X-1, X & X+1 BE THE THREE NUMBERS.
(X-1)X(X+1)=15,600
A SIMPLE TEST CAN DETERMINE THE VALUE OF THE MIDDLE NUMBER.
X^3-X=15,600
X^3=15,600+X
NOW FIND THE CUBE ROOT OF 15,600:
CUBERT15,600=24.98
NOW ADD THE MEXT WHOLE NUMBER ABOVE 24.98 (25) TO 15,600+25=15,625.
NOW FIND THE CUBERT15,625
CUBERT15,625=25 WHICH IS THE MIDDLE NUMBER.
24,25,26 ARE THE 3 NUMBERS.
PROOF:
24*25*26=15,600
15,600=15,600

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