If the product of three consecutive integers is 210, then the sum of integers is .
Created: 1 year ago |
Updated: 6 months ago
Let the three consecutive integers be x, x+1, and x+2.
According to the question, their product is 210. Therefore, we can write:
x(x+1)(x+2) = 210
Expanding the left side, we get:
x3 + 3x2 + 2x - 210 = 0
We can factorize this equation as:
(x-5)(x2 + 8x + 42) = 0
The quadratic factor on the right side has no real roots. Therefore, the only possible value of x is 5.
Hence, the three consecutive integers are 5, 6 and 7.
The sum of these integers is:
5 + 6 + 7 = 18
Therefore, the sum of integers is 18.
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