MathRevolution wrote:

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Math Revolution GMAT math practice question]

Is \(x^3-x>0\)？

\(1) x>1\)

\(2) x>0\)

\({x^3} - x\,\,\mathop > \limits^? \,\,0\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,x\left( {{x^2} - 1} \right)\,\,\mathop > \limits^? \,\,0\,}\,\)

\(\left( 1 \right)\,\,x > 1\,\,\,\, \Rightarrow \,\,\,\left\{ \matrix{

x > 0 \hfill \cr

{x^2} > 1\,\,\,\, \Rightarrow \,\,\,{x^2} - 1 > 0 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle\)

\(\left( 2 \right)\,\,\,x > 0\,\,\,\,\left\{ \matrix{

\,{\rm{Take}}\,\,x = 1\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr

\,{\rm{Take}}\,\,x = 2\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\)

This solution follows the notations and rationale taught in the GMATH method.

Regards,

Fabio.

_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)

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