|(x-y) ² +2(xy+y ²-4y)| = xy+y ²-4y

1 bình luận về “|(x-y) ² +2(xy+y ²-4y)| = xy+y ²-4y”

1. |(x-y)^2 +2(xy+y^2 -4y)|=xy+y^2 -4y

   Do VT=|(x-y)^2 +2(xy+y^2 -4y)|^2 >=0=>xy+y^2 -4y>=0

   =>(x-y)^2 +2(xy+y^2 -4y)>=0

   =>|(x-y)^2 +2(xy+y^2 -4y)|=(x-y)^2 +2(xy+y^2 -4y)

   =>(x-y)^2 +2(xy+y^2 -4y)=xy+y^2 -4y

   <=>(x-y)^2 +(xy+y^2 -4y)=0

   <=> $\{\begin{array}{l}x-y=0\\ xy+y^2-4y=0\end{array}$

   <=> $\{\begin{array}{l}x=y\\ y^2+y^2-4y=0\end{array}$

   <=> $\{\begin{array}{l}x=y\\ 2y(y-2)=0\end{array}$

   <=> $\{\begin{array}{l}x=y\\ [\begin{array}{c}y=0\\ y=2\end{array}\end{array}$

   <=> $[\begin{array}{l}\{\begin{array}{l}x=0\\ y=0\end{array}\\ \{\begin{array}{l}x=2\\ y=2\end{array}\end{array}$ 

   Vậy (x;y)\in {(0;0),(2;2)} 

    

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