MathRevolution wrote:
[
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 :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net