What $3$ integers have a sum of $1$ and a product of $36$
Integers can be negative. I've tried but can't get it. Please help
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6$-2, -3, 6 {}{}{}{}{}{}{}$ is one such triplet. – amWhy Jan 06 '15 at 15:40
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You could pretty quickly list out the combinations of 3 positive numbers whose product is 36. It appears clear that two of the numbers will need to be negative, so find the set where the biggest number is 1 more than the sum of the smallest 2 numbers.
turkeyhundt
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Following turkeyhundt's method, we have (with triples arranged in non-decreasing order) the following:
$$1,1,36 \qquad 1,2,18\qquad 1,3,12\qquad 1,4,9$$
$$1,6,6\qquad \,\,2,2,9\qquad \,\,2,3,6\qquad\,\, 3,3,4$$
By trial and error, the only triples that will satisfy your requirements are the $6$ permutations of the one amWhy found: $$(-2,-3,6)\qquad (-2,6,-3)\qquad (6,-2,-3)$$
$$(-3,-2,6) \qquad (-3,6,-2)\qquad (6,-3,-2)$$
The only other unsigned triple that needed any consideration was $1,6,6$ ...
Zubin Mukerjee
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