a.
\(x+y+\dfrac{1}{x}+\dfrac{1}{y}\ge x+y+\dfrac{4}{x+y}=\left(x+y+\dfrac{1}{x+y}\right)+\dfrac{3}{x+y}\ge2\sqrt{\dfrac{x+y}{x+y}}+\dfrac{3}{1}=5\)
Dấu =" xảy ra khi \(x=y=\dfrac{1}{2}\)
b.
\(x+y+z+\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}\ge x+y+z+\dfrac{9}{x+y+z}=\left(x+y+z+\dfrac{1}{x+y+z}\right)+\dfrac{8}{x+y+z}\)
\(\ge2\sqrt{\dfrac{x+y+z}{x+y+z}}+\dfrac{8}{1}=10\)
Dấu "=" xảy ra khi \(x=y=z=\dfrac{1}{3}\)
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