The product of three consecutive integers is -1716. What is the greatest of the three integers?
2 answers
You can get a very good idea where to start looking by just calculating the cube root of 1716. (The minus sign isn't a problem: it just means that the three consecutive integers will all be negative.)
Let the middle number be x, then the first would be x-1 and the largest would be x+1
so (x-1)(x)(x+1) = -1716
x(x^1 - 1) = -1716
x^3 - x + 1716 = 0
Looking at that tells me that x would be around the cube root of 1716 which is approximately 12, since you said "integer" I will guess at x=12
sure enough 11*12*13 = 1716
so the above would factor to
(x+11)(x+12)(x+13) = 0
so x=-11, x=-12, and x=-13
the greatest of these of course would be the -11
so (x-1)(x)(x+1) = -1716
x(x^1 - 1) = -1716
x^3 - x + 1716 = 0
Looking at that tells me that x would be around the cube root of 1716 which is approximately 12, since you said "integer" I will guess at x=12
sure enough 11*12*13 = 1716
so the above would factor to
(x+11)(x+12)(x+13) = 0
so x=-11, x=-12, and x=-13
the greatest of these of course would be the -11
2 answers