\(x+y+xy=11\Leftrightarrow x\left(y+1\right)+y+1=12\Leftrightarrow\left(x+1\right)\left(y+1\right)=12\)(1)
\(y\left(z+1\right)+z+1=48\Leftrightarrow\left(y+1\right)\left(z+1\right)=48\left(2\right)\)
\(z\left(x+1\right)+x+1=36\Leftrightarrow\left(z+1\right)\left(x+1\right)=36\left(3\right)\)
Lấy vế nhân vế của (1) (2) và (3) ta đc : \(\left[\left(x+1\right)\left(y+1\right)\left(z+1\right)\right]^2=12\cdot36\cdot48=144^2\)
=> \(\left(x+1\right)\left(y+1\right)\left(z+1\right)=144\) hoặc = -144
(+) Với \(\left(x+1\right)\left(y+1\right)\left(z+1\right)=144\)
=> z + 1 = 144 : 12 = 12 => z = 11
=> \(x+1=144:48=3\Rightarrow x=2\)
=> \(y+1=144:36=4\Leftrightarrow y=3\)
(+) Với ( x +1 )( y +1 )( z + 1 ) = -144 ( tương tự )
