Tìm x,y,z: |x-2|+|2x+y-z|+|2z+1|bé hoặc bằng 0 Giúp mình...
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Tìm x,y,z: |x-2|+|2x+y-z|+|2z+1|bé hoặc bằng 0 Giúp mình nhé
\(\left|x-2\right|>=0\forall x\)
\(\left|2x+y-z\right|>=0\forall x,y,z\)
\(\left|2z+1\right|>=0\forall z\)
Do đó: \(\left|x-2\right|+\left|2x+y-z\right|+\left|2z+1\right|>=0\forall x,y,z\)
mà \(\left|x-2\right|+\left|2x+y-z\right|+\left|2z+1\right|< =0\)
nên Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}x-2=0\\2x+y-z=0\\2z+1=0\\\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=2\\z=-\dfrac{1}{2}\\y=-2x+z=-2\cdot2+\dfrac{-1}{2}=-4-\dfrac{1}{2}=-\dfrac{9}{2}\end{matrix}\right.\)