Find the solutions to x⁴-64=0 and the x-intercepts of the graph of y=x⁴-64.

1.

2. and

Step-by-step explanation:

We have the expression to find the solutions we have to clear . Then,

Add 64 in both sides of the equation.

Now we have to re-write the equation:

⇒

Then,

Apply square root on both members

Now substitute back

1.

2.

Solving for x:

1.

2.

Then the solutions for are:

To find the x intercepts of the graph we have to replace with y=0.

This means:

We already found the solutions for the expression, but we have to consider only the real solutions.

Because in a graph we can't have imaginary solutions.

Then the x intercepts of the graph are:

and

The graph of the function is:

6 equilateral triangles