Question

Graph y = x 3 and y = 16/x on the same set of coordinate axes. Use the graphs to find the exact solutions to the equation x 3 = 16/x . Verify by substitution that they satisfy the equation.

Answer 1

This is the same as the first answer but you can copy and paste this one :)

Explanation:

Given : Equations y=x^3 and y=16/x

To find : Graph both the equations and Use the graphs to find the exact solutions to the equation x^3=16/x

Solution : Let, [1] y=x^3 and [2] y=16/x

Now, we plot these two equations.

The graph of y=x^3 is shown with green line.

The graph of y=16/x is shown with violet line.

Now, using the graph,

The solution to this system will be their intersection point.

The intersection points are (2,8) and (-2,-8).

If we substitute y from [1] equation into [2]

We get, x^3=16/x

Answer 2

Refer the attached figure.

Explanation:

Given : Equations
`y=x^3` and
`y=(16)/(x)`

To find : Graph both the equations and Use the graphs to find the exact solutions to the equation
`x^3=(16)/(x)`

Solution :

Let,
`y=x^3` ........[1]

`y=(16)/(x)` .......[2]

Now, we plot these two equations.

The graph of
`y=x^3` is shown with green line.

The graph of
`y=(16)/(x)` is shown with violet line.

Now, using the graph,

The solution to this system will be their intersection point.

The intersection points are (2,8) and (-2,-8).

If we substitute y from [1] equation into [2]

We get,
`x^3=(16)/(x)`

Refer the attached figure below.