x real number
compare this numbers :
Consider different cases:
Case 1: If $\displaystyle x>1$, (eg: 3)
$\displaystyle x^3>x^2>x$
Case 2: If $\displaystyle x=1$,
$\displaystyle x^3=x^2=x$
Case 3: If $\displaystyle 0<x<1$, (eg: 0.5)
$\displaystyle x>x^2>x^3$
Case 4: If $\displaystyle x=0$,
$\displaystyle x^3=x^2=x$
Case 5: If $\displaystyle -1<x<0$, (eg: -0.5)
$\displaystyle x^2>x^3>x$
Case 6: If $\displaystyle x=-1$,
$\displaystyle x^2>x^3=x$
Case 7: If $\displaystyle x<-1$, (eg: -3)
$\displaystyle x^2>x>x^3$