enigma123 wrote:
Does the product jkmn equals 1?
(1) \(\frac{jk}{mn} = 1\)
(2) \(mn>7\)
\(jkmn\,\,\mathop = \limits^? \,\,1\)
\(\left( 1 \right)\,\,\,{{jk} \over {mn}} = 1\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {j,k,m,n} \right) = \left( {1,1,1,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {j,k,m,n} \right) = \left( {2,2,2,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.\)
\(\left( 2 \right)\,\,\,mn > 7\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {j,k,m,n} \right) = \left( {1,8,1,8} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {j,k,m,n} \right) = \left( {{1 \over 8},1,1,8} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\)
\(\left( {1 + 2} \right)\,\,\,\,\,?\,\,\,:\,\,\,jkmn\,\, = \,\,\left( {jk} \right)\left( {mn} \right)\,\,\,\mathop = \limits^{\left( 1 \right)} \,\,\,{\left( {mn} \right)^2}\,\,\,\mathop > \limits^{\left( 2 \right)} \,\,\,{7^{\,2}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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