The product of three consecutive odd integers is 4845. What is the largest of these three integers?
actually, that would help if the sum were 4845.
In this case, if all three factors were equal, they would be ∛4845 ≈ 17
So, I'd try 15*17*19 = 4845
Let's assume the three consecutive odd integers are x, x+2, and x+4.
According to the given information, the product of these three integers is 4845. So we can write the equation:
x * (x+2) * (x+4) = 4845
Expanding the equation:
(x^2 + 2x) * (x+4) = 4845
x^3 + 6x^2 + 8x - 4845 = 0
Now, we can solve this equation to find the value of x. Once we find x, we can determine the largest of the three consecutive integers by adding 4 to x.
Using a calculator or a software, we find that x is approximately 15.
So, the three consecutive odd integers are: 15, 17, and 19.
Therefore, the largest of these three integers is 19.
To find the largest of the three consecutive odd integers, we need to first determine the three consecutive odd integers whose product is 4845.
Let's assume the first odd integer is x. Since the integers are consecutive, the next two odd integers would be x+2 and x+4.
To find the product of these three consecutive odd integers, we can multiply them together:
x * (x+2) * (x+4) = 4845
Now we have a quadratic equation that we can solve to find the value of x.
Expanding the expression:
(x^2 + 2x) * (x+4) = 4845
Simplifying further:
x^3 + 6x^2 + 8x - 4845 = 0
Now, we can solve this equation to find the value of x. This can be done by using numerical methods or finding the roots of the equation.
Once we find the value of x, we can determine the consecutive odd integers and identify the largest one.
Divide 4845 by 3.
That gives you a good start.