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x^2=>x???

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x^2=>x??? [#permalink] New post 24 May 2013, 14:15
x^2 > x
=> x^2-x>0
=> x(x-1)>0
so x>0 or x>1.

Just curious x<0 also is valid for the above equation but when I solve mathematically I don't seem to get this as an option
Can you plase let me know where I am going wrong.

Thanks
gmatrant
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Re: x^2=>x??? [#permalink] New post 24 May 2013, 21:39
gmatrant wrote:
x^2 > x
=> x^2-x>0
=> x(x-1)>0
so x>0 or x>1.

Just curious x<0 also is valid for the above equation but when I solve mathematically I don't seem to get this as an option
Can you plase let me know where I am going wrong.

Thanks
gmatrant

Hi,

x(x-1)>0 means, x<0 or x>1
for 0<x<1, x(x-1) < 0
Please check the post Solving Inequalities

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Re: x^2=>x??? [#permalink] New post 25 May 2013, 02:19
Expert's post
gmatrant wrote:
x^2 > x
=> x^2-x>0
=> x(x-1)>0
so x>0 or x>1.

Just curious x<0 also is valid for the above equation but when I solve mathematically I don't seem to get this as an option
Can you plase let me know where I am going wrong.

Thanks
gmatrant


x^2>x --> x(x-1)>0. Both multiple must have the same sign:

x>0 and x-1>0 (x>1), so x>1.
x<0 and x-1<0 (x<1), so x<0.

Thus x^2>x holds true for x<0 and x>1.

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html?hilit=extreme#p868863
xy-plane-71492.html?hilit=solving%20quadratic#p841486

Hope it helps.
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Re: x^2=>x???   [#permalink] 25 May 2013, 02:19
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