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Which is correct?

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by frank1 » Thu May 20, 2010 5:54 am
X ^ 2> X ^ 3,
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by saurabhmahajan » Thu May 20, 2010 6:01 am
Yeap it should be X ^ 2> X ^ 3
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by colakumarfanta » Thu May 20, 2010 6:07 am
I guess X ^ 2> X ^ 3 is also not true when X = 0 . Please let me know if I am missing anything ?
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by Rahul@gurome » Thu May 20, 2010 8:50 pm
Solution.
Obviously x^2 > x^3 does not hold for x = 0.
Taking the second statement we have that (X +1 / 2) (X-1 / 2) <0
So we have that either (a) (X +1 / 2)>0 and (X-1 / 2)< 0
Or
(b) (X +1 / 2)<0 and (X-1 / 2)>0. This would mean x<-1/2 and x>1/2 which is not possible and so (b) is automatically rejected.
So we have that (X +1 / 2) (X-1 / 2) <0 implies -1/2<x<1/2 which is possible because given range of x is -1 <x<1.

The second statement is true.
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by quantskillsgmat » Fri May 21, 2010 2:52 am
first statement doesnt hold always put x=0
for second statement x should be between -1/2 and 1/2.since range of x is between -1 and 1.so it is always true.
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