How do you solve #2X^3-x^4<=0#?

1 Answer
Jan 6, 2017

Answer:

The values for #x# that are solutions are #x>=2" and "x<=0#

Written another way #x in(-oo,0color(white)(.)] " and "x in [color(white)(.)2,+oo)#

Explanation:

Given:#" "2x^3-x^4<=0#

#x^3(2-x)<=0#

Suppose #x>=2# then #(2-x)<=0# so #x^3(2-x)<=0#
Consequently #x>=2# is part of the answer

Suppose #x=0# then #x^3(2-x)=0# which satisfies the #<=0# criterion. Consequently #x=0# is part of the solution.

Suppose #x<0# then #x^3<0# and #(2-x)>0# so their product is #<0# thus satisfying the criterion #<=0#

So the value for #x# that are solutions are #x>=2" and "x<=0#

Tony B