Question

Malaya was told that the volume of a box that is a cube is 4,096 cubic inches. She knows the formula for the

volume of a cube with side length x is V(x) = x^3, so she models the volume of the box with the equation
x^3 − 4096 = 0.
a. Solve this equation for x.
b. Malaya shows her work to Tiffany and tells her that she has found three different values for the side length of
the box. Tiffany looks over Malaya’s work and sees that it is correct but explains to her that there is only one
valid answer. Help Tiffany explain which answer is valid and why.

Answer 1

a) x = 16 is the only possible solution of equation.

Explanation:

Here, the given equation of Volume V(x) =
`x^(3)  - 4096`

a) To solve the equation:
`x^(3)  - 4096  = 0`

Now solving this equation, we get

`x^(3)  =  4096`

Taking cube roots both sides, we get

`x = \sqrt[3]{4096}` or,
`x = \sqrt[3]{16  * 16 * 16}`

So, solving this we get x = 16 is the only possible solution of equation.

b) There is not any other possible solution to the given equation.