How do you evaluate #3x ^ { 2/ 3} + 8x ^ { 1/ 3} + 5= 0#?

1 Answer

#-125/27,-1#.

Explanation:

Suppose,#x^⅓=a#

Then resolve the equation,
#3a^2+8a+5=0#:

#(3a+5)(a+1)=0#

#a=-5/3, -1#

Substitute back in:

#x^(1/3)=-5/3,-1=>x=(-5/3)^3,(-1)^3=-125/27,-1#

graph{3x^(2/3)+8x^(1/3)+5 [-14.455, 5.545, -1.36, 8.64]}