SOLUTION: Please solve: x^6-64 = 0

Question 119631This question is from textbook Trigonometry
: Please solve:
x^6-64 = 0 This question is from textbook Trigonometry

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Factor the left side by using the difference of cubes formula

Factor to get

Now set each factor equal to zero:

, or

Now solve for x for the first two factors:

, or

So the first two roots are or

-------------

Now let's solve

Let

Let's use the quadratic formula to solve for w:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=4, and c=16

Square 4 to get 16

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

After simplifying, the quadratic has roots of

or

Remember, . So or

Now take the square root of both sides for each case

or

Now break up the plus/minus

, , , or

So the roots of are

, , , or , or
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