Bunuel wrote:

What is the value of x^4y^2 - x^4/y^2 ?

(1) x = 2y

(2) y = 1

\(?\,\,\,\, = \,\,\,\,{x^4}{y^2} - {{{x^4}} \over {{y^2}}}\,\,\,\, = \,\,\,\,{x^4}\left( {{y^2} - {1 \over {{y^2}}}} \right)\)

\(\left( 1 \right)\,\,x = 2y\,\,\,\,\left\{ \matrix{

\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {2,1} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \,\,\,{2^{\,4}}\left( {1 - 1} \right) = 0 \hfill \cr

\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4,2} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \,\,\,{4^{\,4}}\left( {4 - {1 \over 4}} \right) \ne 0\,\, \hfill \cr} \right.\)

\(\left( 2 \right)\,\,y = 1\,\,\,\,\, \Rightarrow \,\,\,\,\,\,?\,\, = \,\,{x^4} \cdot \left( {1 - {1 \over 1}} \right)\,\, = \,\,0\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.\,\,\,\,\,\,\)

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

Regards,

Fabio.

_________________

Fabio Skilnik :: https://www.GMATH.net (Math for the GMAT)

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