Question #3e005
2 Answers
Dec 19, 2017
Explanation:
First, move the parts to opposite sides, leading to:
Then, cube root both sides.
This leads to
Dec 19, 2017
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"