If x^3 0 ?

Question

If x^3 < x^2 , is x > 0 ? A. |x|<1 B. x > x^2

chetan2u · Answer

x^3 < x^2........x^3-x^2<0......x^2(x-1)<0 x^2 will always be non negative, therefore x-1<0 or x<1... So we know X<1, we have to check if it is between 0 and 1 or not.. 1) |x|<1... This can be written as -1x^2... If the number is negative, it's square will be positive and hence square will always be greater than the number itself. Therefore, the number is not negative and will be between 0 and 1.. Sufficient.. Also x>x^2.....X(1-x)>0 ... Two cases.. if x is negative, 1-x too has to be negative. But 1-x will always be positive if x<0... So x has to be positive.. and 1-x>0...X<1 B

AnisMURR · Answer

Thank you chetan2u

But i have a small thing to mention. It doesn't affect your solution but. If x^3 < x^2 this does not mean that x<1 because when x = 0 both quantities are equal. Best,

chetan2u · Answer

Hi..
Yes, I have mentioned that X is between 0 to 1. So both X and 1 is not included
If my solution included 0, I would have written it as 'from 0 to 1'. Here both would be included.

If x^3 < x^2, is x > 0 ?

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