a.
\(4A=\left(x+4-x\right)\left(\dfrac{1}{x}+\dfrac{1}{4-x}\right)\ge\left(\dfrac{1}{\sqrt{x}}.\sqrt{x}+\dfrac{1}{\sqrt{4-x}}.\sqrt{4-x}\right)^2=4\)
\(\Rightarrow A\ge1\)
\(A_{min}=1\) khi \(x=2\)
b.
\(3B=\left(2x+3-2x\right)\left(\dfrac{2}{2x}+\dfrac{1}{3-2x}\right)\ge\left(\sqrt{\dfrac{2}{2x}}.\sqrt{2x}+\dfrac{1}{\sqrt{3-2x}}.\sqrt{3-2x}\right)^2=3+2\sqrt{2}\)
\(\Rightarrow B\ge\dfrac{3+2\sqrt{2}}{3}\)
Dấu "=" xảy ra khi \(x=\dfrac{6-3\sqrt{2}}{2}\)
c.
\(2C=\left(3x-3+5-3x\right)\left(\dfrac{3}{3x-3}+\dfrac{1}{5-3x}\right)\ge\left(\sqrt{\dfrac{3}{3x-3}}.\sqrt{3x-3}+\dfrac{1}{\sqrt{5-3x}}.\sqrt{5-3x}\right)^2=4+2\sqrt{3}\)
\(\Rightarrow C\ge2+\sqrt{3}\)
Dấu "=" xảy ra khi \(x=\dfrac{6-\sqrt{3}}{3}\)
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