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Find three consecutive natural numbers, whose product is 81204. (Select the equation.)

n x (n+1) x (n+2) = 81204 ?

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1  
What? Is this question complete? – Omer Hassan Mar 14 '12 at 12:58
What do you mean for 'output'? – Riccardo.Alestra Mar 14 '12 at 13:02
output = product ? output = sum ? – lhf Mar 14 '12 at 13:02
output = product ?...yes is product – Klea Gega Mar 14 '12 at 13:05
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The equation $(n-1)n(n+1)=n^3-n=81204$ does not have an integer solution. – lhf Mar 14 '12 at 13:17
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closed as not a real question by t.b., lhf, Asaf Karagila, Benjamin Lim, Nate Eldredge Mar 14 '12 at 14:33

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.

5 Answers

up vote 1 down vote

You wish to solve $n(n+1)(n+2)=81204$. If there is a solution, then $n$ is approximately $\root 3\of {81204}\approx 43.3$. Now checking possible solutions:

$\ \ \ 42\cdot43\cdot44=79464$

$\ \ \ 43\cdot44\cdot 45=85140$

None of these work, but these are the only possible solutions (other choices would give you something less than $79464$ or something greater than $85140$). So there is no solution to your problem.

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up vote 0 down vote

Hint: if the first number is $n$, what are the next two?

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n x (n+1) x (n+2) = 81204 – Klea Gega Mar 14 '12 at 13:09
1  
@KleaGega: From the wording, it looked like a multiple choice question, this should have been one of the choices. You are correct. The fact that the equation has no solution in the integers doesn't change the fact that the equation is the correct formulation of the problem. – Ross Millikan Mar 14 '12 at 14:19
up vote 0 down vote

27067 + 27068 + 27069 = 81204

81205 + 81206 - 81207 = 81204

But really I have no idea what your question really means.

Edit: Okay you want the product. I recommend you try trial and error to find the value of n if it exists.

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n x (n+1) x (n+2) = 81204 – Klea Gega Mar 14 '12 at 13:09
up vote 0 down vote

n*(n+1)*(n+2)=81204

expand this equation to get: n^3 + 3n^2 + 2n - 81204 = 0

use this 3rd degree Calculator, to get these answers:

42.31147753802359 -22.655738769011794 + 37.49550726280472 i -22.655738769011794 - 37.49550726280472 i

the answers are not integers. (refer to your quest)

or check this site to know the technique of solving a third degree eqn.

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up vote -1 down vote

number1 = n number2 = n + 1 number3 = n + 2 sum = number1 + number2 + number3 81204 = n + (n + 1) + (n + 2) 81204 = 3n + 3 81201 = 3n n = 27067 solution: {27067, 27068, 27069}

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n x (n+1) x (n+2) = 81204 – Klea Gega Mar 14 '12 at 13:08

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