BhaveshGMAT wrote:
adiagr wrote:
\(x^2(x^2 - 1)> 0\)
x^2 is always positive.
So the condition is
\(x^2 - 1> 0\)
Can anyone please clarify my doubt here?
I generally solve such questions using number line after I have simplified to get individual values of x.
I fail to understand how x^2 has been eliminated here. What's troubling me here is that I denoted 'zero' on the number line.
In the original question, we know |x| < x^2. So it's impossible that x = 0, because x = 0 doesn't satisfy that inequality.
There are a lot of ways to solve the original question, but if you did end up with the inequality
\(x^2(x^2 - 1)> 0\)
then since x^2 is always a positive number (we know x is not zero), we can safely divide both sides of the inequality by x^2. Since x^2 must be positive, we don't need to worry about whether we might be dividing by a negative number, so we don't need to worry about whether we should reverse the inequality. And once you divide by x^2, you learn x^2 - 1 > 0, or x^2 > 1.
I don't think that approach is the best one to take on questions like this, but I'll assume other approaches were already explained earlier in the thread (I haven't read all the solutions).
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