Is x^3

Question

If you look at x^3 < X^2<0, then it has solution X<1 except X=0

but when same equation is rearranged to:
X(X^2 -1)<0, the solution is 0<X<1 and X< -1. For -1<X<0, the equation is not satisfied as it yields positive value, eg x= -1/2, then X(X^2 -1)<0 yeilds
positive value, therefore solution -1<X<0 is not possible. But from equation x^3 < X^2, which is the same the equation, the solution includes the value -1<X<0
as well.

So the equation is same and when you arrange it the solutions are different why?...(is it due to some sign constraints)

IanStewart · Answer

if you start from this inequality:

x^3 < x^2

and subtract x^2 on both sides, you get

x^3 - x^2 < 0

Now you can factor out x^2 to get:

x^2 ( x - 1) < 0

You'll find this inequality has the same solutions as the original one. There's an error in the factorization in your post, which is the reason your two inequalities have different solutions - you arrived at x (x^2 - 1) < 0, which is not the same as your original inequality.

IanStewart · Answer

Incidentally, there's no advantage in this particular question to doing any rearrangement. If we know:

x^3 < x^2

we can just divide both sides by x^2; because x^2 can't be negative, we don't need to worry about whether to flip the inequality. So we get:

x < 1

But since we're not allowed to divide by 0, we have to check whether x = 0 ought to be a solution too, by plugging it into the original inequality, and it shouldn't be, so the solutions are 0 < x < 1 and x < 0.

Supermaverick · Answer

Thanks , I made a mistake while factoring.

Is x^3 < X^2 and X(X^2 -1)< 0 have same solution?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards