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a/ \(P=3x+\frac{1}{2x}=\frac{x}{2}+\frac{5x}{2}+\frac{1}{2x}\) \(\ge2\sqrt{\frac{x}{2}.\frac{1}{2x}}+\frac{5.1}{2}=\frac{5}{2}\)
"="\(\Leftrightarrow x=1\)
b/ \(B=\frac{3x}{2}+\frac{1}{x+1}=\frac{3\left(x+1\right)}{2}-\frac{3}{2}+\frac{1}{x+1}\)
\(\ge2\sqrt{\frac{3\left(x+1\right)}{2}.\frac{1}{x+1}}-\frac{3}{2}=\frac{-3+2\sqrt{6}}{2}\)
"="\(\Leftrightarrow3\left(x+1\right)^2=2\Leftrightarrow x=\frac{-3+\sqrt{6}}{3}\)
c/ \(C=\frac{x}{3}+\frac{5}{2x-1}=\frac{2x-1}{6}+\frac{1}{6}+\frac{5}{2x-1}\)
\(\ge2\sqrt{\frac{2x-1}{6}.\frac{5}{2x-1}}+\frac{1}{6}=\frac{1+4\sqrt{15}}{6}\)
"="\(\Leftrightarrow x=\frac{6+\sqrt{30}}{12}\)
d/ \(D=\frac{x^2+4x+4}{x}=x+4+\frac{4}{x}\)\(\ge2\sqrt{x.\frac{4}{x}}+4=8\)
"="\(\Leftrightarrow x=2\)
a/ \(\frac{x}{2}+\frac{1}{2x}+\frac{5}{2}x\ge2\sqrt{\frac{x}{2}.\frac{1}{2x}}+\frac{5}{2}.1=\frac{7}{2}\)
\("="\Leftrightarrow x=1\)
b/ \(B=\frac{3\left(x+1\right)}{2}+\frac{1}{x+1}-\frac{3}{2}\ge2\sqrt{\frac{3\left(x+1\right)}{2\left(x+1\right)}}-\frac{3}{2}=\frac{-3+2\sqrt{6}}{2}\)
\("="\Leftrightarrow\left(x+1\right)^2=\frac{2}{3}\Rightarrow x=\frac{-3+\sqrt{6}}{3}\)
c/ \(C=\frac{2x-1}{6}+\frac{5}{2x-1}+\frac{1}{6}\ge2\sqrt{\frac{\left(2x-1\right).5}{6\left(2x-1\right)}}+\frac{1}{6}=\frac{1+2\sqrt{30}}{6}\)
\("="\Leftrightarrow\left(2x-1\right)^2=30\Rightarrow x=...\)
d/ \(D=x+\frac{4}{x}+4\ge2\sqrt{x.\frac{4}{x}}+4=8\)
\("="\Leftrightarrow x^2=4\Rightarrow x=...\)
Chi biet phan 5 thoi @
Vi 3a=5b=12suy ra a=4 ;b=2,4 ta co p=a.b suy ra p=4×2.4=9.6 suy ra p>[=9.6 gtln=9.6
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a/ \(A=\frac{x}{2}+\frac{1}{2x}+\frac{5x}{2}\ge2\sqrt{\frac{x}{4x}}+\frac{5}{2}.1=\frac{7}{2}\)
\("="\Leftrightarrow x=1\)
b/ \(B=\frac{3\left(x+1\right)}{2}+\frac{1}{x+1}-\frac{3}{2}\ge2\sqrt{\frac{3\left(x+1\right)}{2\left(x+1\right)}}-\frac{3}{2}=\frac{-3+2\sqrt{6}}{2}\)
\("="\Leftrightarrow\left(x+1\right)^2=\frac{2}{3}\Rightarrow x=...\)
c/ \(C=\frac{2x-1}{6}+\frac{5}{2x-1}+\frac{1}{6}\ge2\sqrt{\frac{5\left(2x-1\right)}{6\left(2x-1\right)}}+\frac{1}{6}=\frac{1+2\sqrt{30}}{6}\)
\("="\Leftrightarrow\left(2x-1\right)^2=30\Rightarrow x=...\)
d/ \(D=x+\frac{4}{x}+4\ge2\sqrt{\frac{4x}{x}}+4=8\)
\("="\Leftrightarrow x^2=4\Rightarrow x=...\)
e/ \(E=\left(x+3\right)\left(5-x\right)\le\frac{1}{4}\left(x+3+5-x\right)^2=16\)
\("="\Leftrightarrow x+3=5-x\Rightarrow x=...\)
f/ \(F=\frac{1}{2}\left(2x+6\right)\left(5-2x\right)\le\frac{1}{8}\left(2x+6+5-2x\right)^2=\frac{121}{8}\)
\("="\Leftrightarrow2x+6=5-2x\Leftrightarrow x=...\)