the product of three consecutive positive integers is 35,904. what is the sum of the three integers?

To find the sum of the three consecutive positive integers, we first need to determine what those integers are.

Let's assume the first integer is 'x'. Then the next two consecutive positive integers would be 'x + 1' and 'x + 2'.

According to the given information, the product of these three integers is 35,904. Hence, we can form the following equation:

x * (x + 1) * (x + 2) = 35,904

Now, we can solve this equation to find the value of 'x'.

x^3 + 3x^2 + 2x - 35,904 = 0

To solve this cubic equation, we can use either a numerical or algebraic method. However, in this case, using a numerical method such as trial and error or a calculator would be the easiest approach.

By observing different values for 'x', we can find that when 'x = 48', the equation satisfies the condition:

48 * (49) * (50) = 35,904

Now that we know the value of 'x', we can calculate the sum of the three consecutive positive integers:

Sum = x + (x + 1) + (x + 2) = 48 + 49 + 50 = 147.

Therefore, the sum of the three consecutive positive integers is 147.