\(P=2x+y+\dfrac{30}{x}+\dfrac{5}{y}=\left(x+y\right)+\left(\dfrac{5}{x}+\dfrac{5}{y}\right)+\left(\dfrac{25}{x}+x\right)\)
\(\left\{{}\begin{matrix}x>0\Rightarrow x=\left(\sqrt{x}\right)^2\\y>0\Rightarrow y=\left(\sqrt{y}\right)^2\end{matrix}\right.\)
\(P_1=x+y\ge10\)
\(P_2=\dfrac{5}{x}+\dfrac{5}{y}=5.\left(\dfrac{1}{x}+\dfrac{1}{y}\right)\ge5.\dfrac{4}{x+y}=\dfrac{5.4}{10}=2\) khi x =y
\(P_3=\dfrac{25}{x}+x\ge2.\sqrt{\dfrac{25}{x}.x}=2.5=10\) khi x =5
\(P=\sum P\ge10+2+10=22\) khi (x;y) =(5;5)
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