the product of three consecutive numbers is 4080. what are the numbers?
What is the cube root of 4080?
http://www.csgnetwork.com/cuberootcubecalc.html
Take it from there.
please give better explanation, if possible.
Did you find the cube root of 4080?
What is it?
If we say that the middle value is n
then
(n-1)n(n+1)=4080
so
n^3-n-4080=0
there are the several approaches to use.
Using Ms Sue's approach is to say that
n is approximately cuberoot(4080)=15.98
we can then use 16 and adjust from there. Luckily (?) we then find the three numbers are 15, 16, 17.
Does this help?
yes' thank you. i'm trying to help my grandaughter with her 6 grade math summer project.
To find three consecutive numbers whose product is 4080, we can follow these steps:
Step 1: Let's assume the first number as (x-1), the second number as x, and the third number as (x+1).
Step 2: According to the given information, the product of the three consecutive numbers is 4080. Therefore, we can write the equation as: (x-1) * x * (x+1) = 4080.
Step 3: Simplify the equation: x * (x^2 - 1) = 4080.
Step 4: Expand further: x^3 - x = 4080.
Step 5: Rearrange the equation: x^3 - x - 4080 = 0.
Now that we have a cubic equation, we need to solve it to find the value of x, which corresponds to the second number in our sequence.
There are several methods to solve cubic equations, such as factoring, using the rational root theorem, or using numerical methods like Newton's method.
Factoring: Try finding a factor or a root that simplifies the equation. In this case, finding integers that are factors of 4080 can help to narrow down potential solutions.
Using the rational root theorem: This theorem states that any rational root of the equation will have the form p/q, where p is a factor of the constant term (in this case, 4080) and q is a factor of the leading coefficient (which is 1 in this case).
Using numerical methods: If factoring and the rational root theorem do not yield any rational solutions, one can use numerical methods like Newton's method or numerical root-finding algorithms to approximate the roots.
Once we find the value of x, we can easily determine the other two consecutive numbers by subtracting one and adding one to the value of x obtained.