The product of 3 consecutive odd numbers is 2,145
x(x^2-4) = 2145
11(13(15 = 2145
or, since the ∛2145 = 12.89 and three consecutive odd numbers are pretty close to each other,
13^3 = 2197
which is pretty close. So pick 13 as the middle number
To find the three consecutive odd numbers whose product is 2,145, we can use the following steps:
Step 1: Let's assume the first odd number as "x."
Step 2: The next odd number will be "x + 2" since consecutive odd numbers have a difference of 2.
Step 3: The third odd number will be "x + 4" following the same pattern.
Step 4: To find the product of these three numbers, we multiply them together:
x * (x + 2) * (x + 4) = 2,145.
Step 5: Simplify the equation:
x^3 + 6x^2 + 8x - 2,145 = 0.
Now, we can use various methods to solve this equation and find the value of "x".
To find the three consecutive odd numbers whose product is 2,145, we can use algebra.
Let's assume the first odd number as 'x'. Then the second consecutive odd number would be 'x + 2', and the third consecutive odd number would be 'x + 4'.
According to the given information, the product of these three numbers is 2,145:
x * (x + 2) * (x + 4) = 2,145
Now we can solve this equation to find the value of 'x'. By simplifying and rearranging the equation, we get:
x^3 + 6x^2 + 8x - 2,145 = 0
This equation is a cubic equation, which can be challenging to solve directly. However, we can use different methods to find the roots of this equation, such as factoring, using the Rational Root Theorem, or using numerical methods.
One common numerical method is to use a graphing calculator or computer software to graph the equation and find the x-intercepts. This will help us approximate the solutions.
By using an equation solver, we find that x ≈ 11.445. Since we are looking for consecutive odd numbers, the closest integer to 11.445 would be 11.
Therefore, the three consecutive odd numbers that have a product of 2,145 are:
11, 13, and 15.