$tu gt :3x^{2}+3y^{2}+7z^{2}+4xy+2yz=3-p^{2} co: x^{2}+4z^{2}\geq 4xz,y^{2}+z^{2}\geq 2zy \Rightarrow 2x^{2}+2z^{2}+2y^{2}+4yz+4xz+4xy\leq 3-p^{2} \Rightarrow 2p^{2}\leq 3-p^{2} \ Rightarrow p^{2}\leq 1 \Rightarrow -1\leq p\leq 1 \Rightarrow min p= -1\Leftrightarrow x=\frac{-1}{2},y= z= \frac{-1}{4} , max p=1\Leftrightarrow x= \frac{1}{2},y= z= \frac{1}{4}$
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