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"#