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If the sum of three consecutive integers is equal to their product ,then find the integers?
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If the sum of three consecutive integers is equal to their product ,th...
Problem: If the sum of three consecutive integers is equal to their product, then find the integers.

Solution:

Let the three consecutive integers be x, x+1, and x+2.

According to the problem, we have:

x + (x+1) + (x+2) = x(x+1)(x+2)

Simplifying the left side:

3x + 3 = x^3 + 3x^2 + 2x

Simplifying the right side:

x^3 + 3x^2 + 2x = x^2(x+2) + x(x+2) = x(x+1)(x+2)

Therefore, we have:

3x + 3 = x(x+1)(x+2)

Expanding the right side:

3x + 3 = x^3 + 3x^2 + 2x

Subtracting 3x + 3 from both sides:

0 = x^3 + 3x^2 + 2x - 3x - 3

Simplifying:

0 = x^3 + 3x^2 - x - 3

We can solve this equation by trying different values of x. We find that x=1 is a solution.

Therefore, the three consecutive integers are:

1, 2, and 3

Answer: The three consecutive integers are 1, 2, and 3.
Community Answer
If the sum of three consecutive integers is equal to their product ,th...
It's 1,2&3.
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If the sum of three consecutive integers is equal to their product ,then find the integers?
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