Question

Question #3e005

Answer 1

`x=4`

Explanation:

First, move the parts to opposite sides, leading to:
`64=x^3`

Then, cube root both sides.
`root(3)64=root(3)(x^3)`

This leads to
`4=x`

Answer 2

`x=4" or "x=-2+-2sqrt3i`

Explanation:

`x^3-64" is a "color(blue)"difference of cubes"`

`•color(white)(x)a^3-b^3=(a-b)(a^2+ab+b^2)`

`"here "a=x" and "b=4`

`rArrx^3-64=(x-4)(x^2+4x+16)=0`

`"equate each factor to zero and solve for x"`

`x-4=0rArrx=4larrcolor(red)"real root"`

`"solve "x^2+4x+16 " using the "color(blue)"quadratic formula"`

`"with "a=1,b=4" and "c=16`

`x=(-4+-sqrt(16-64))/2`

`color(white)(x)=(-4+-sqrt(-48))/2=(-4+-4sqrt3i)/2`

`rArrx=-2+-2sqrt3ilarrcolor(red)"complex roots"`