Question #3e005

2 Answers
Dec 19, 2017

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

Dec 19, 2017

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"