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

Question

2462 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-06T16:23:35

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

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

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

How do you solve 2X^3-x^4<=02X^3-x^4<=0?