Tính M = 1 + log 12 x + log 12 y 2 log 12 ( x + 3 y ) .

Ta có \({x^2} + 9{y^2} = 6xy\)\( \Leftrightarrow {\left( {x + 3y} \right)^2} = 12xy\)\( \Leftrightarrow {\log _{12}}{\left( {x + 3y} \right)^2} = {\log _{12}}\left( {12xy} \right)\)

\( \Leftrightarrow 2{\log _{12}}\left( {x + 3y} \right) = {\log _{12}}12 + {\log _{12}}x + {\log _{12}}y\)\( \Leftrightarrow M = \frac{{{{\log }_{12}}12 + {{\log }_{12}}x + {{\log }_{12}}y}}{{2{{\log }_{12}}\left( {x + 3y} \right)}} = 1\)

Trả lời: 1.