\(P=\dfrac{2012}{x^2+4x+2013}\)
\(P_{MAX}\Rightarrow x^2+4x+2013_{MIN}\)
\(\Rightarrow x^2+4x+2013=1\)
\(P_{MIN}=\dfrac{2012}{1}=2012\)
\(Q=\dfrac{a^{2012}+2013}{a^{2012}+2011}\)
\(Q=\dfrac{a^{2012}+2011+2}{a^{2012}+2011}=\dfrac{a^{2012}+2011}{a^{2012}+2011}+\dfrac{2}{a^{2012}+2011}\)
\(Q=1+\dfrac{2}{a^{2012}+2011}\)
\(a^{2012}\ge0\)
\(Q_{MAX}\Rightarrow a^{2012}_{MIN}=0\)
\(\Rightarrow Q_{MAX}=1+\dfrac{2}{2011}=\dfrac{2013}{2011}\)
a)\(P=\dfrac{2012}{x^2+4x+2013}\)
Ta thấy: \(x^2+4x+2013=x^2+4x+4+2009\)
\(=\left(x+2\right)^2+2009\ge2009\)
\(\Rightarrow\dfrac{1}{\left(x+2\right)^2+2009}\le\dfrac{1}{2009}\)
\(\Rightarrow P=\dfrac{2012}{\left(x+2\right)^2+2009}\le\dfrac{2012}{2009}\)
Xảy ra khi \(x=-2\)