\(B=y^2-y+\dfrac{12}{y}+2016\)
\(B=y^2-4y+4+3y+\dfrac{12}{y}+2012\)
\(B=\left(y^2-4y+4\right)+3\left(y+\dfrac{4}{y}\right)+2012\)
\(B=\left(y-2\right)^2+3\left(y+\dfrac{4}{y}\right)+2012\)
Theo BĐT Cauchy \(y+\dfrac{4}{y}\ge2\sqrt{y\cdot\dfrac{4}{y}}=2\cdot\sqrt{4}=2\cdot2=4\)
Mà: \(\left(y-2\right)^2\ge0\)
\(\Leftrightarrow B=\left(y-2\right)^2+3\left(y+\dfrac{4}{y}\right)+2012\ge0+3\cdot4+2012=2024\)
Vậy Bmin = 2024
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