*)Minimize : Áp dụng BĐT \(\sqrt{a}+\sqrt{b}\ge\sqrt{a+b}\) ta có:
\(M=\sqrt{x-1}+\sqrt{y+3}\)
\(\ge\sqrt{x-1+y+3}=\sqrt{x+y+2}=\sqrt{10}\)
Xảy ra khi \(x=1;y=7\)
*)Maximize: Áp dụng BĐT Cauchy-Schwarz ta có:
\(M^2=\left(\sqrt{x-1}+\sqrt{y+3}\right)^2\)
\(\le\left(1+1\right)\left(x-1+y+3\right)\)
\(=2\left(x+y+2\right)=2\cdot\left(8+2\right)=20\)
\(\Rightarrow M^2\le20\Rightarrow M\le\sqrt{20}\)
Xảy ra khi \(x=6;y=2\)
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