Question

Câu 1 : Tìm GTLN

a) \(A=\dfrac{2003}{\left(x-2\right)^2+\left(x-y\right)^6+3}\)

b) \(B=3-\left(2x+\dfrac{1}{3}\right)^6\)

c) \(C=\dfrac{x^{2016}+2017}{x^{2016}+2015}\)

Answer 1

a: \(\left(x-2\right)^2+\left(x-y\right)^6+3\ge3\)

\(\Leftrightarrow A=\dfrac{2003}{\left(x-2\right)^2+\left(x-y\right)^6+3}\le\dfrac{2003}{3}\)

Dấu '=' xảy ra khi x=y=2

b: \(B=-\left(2x+\dfrac{1}{3}\right)^6+3\le3\forall x\)

Dấu '=' xảy ra khi x=-1/6

c: \(C=\dfrac{x^{2016}+2015+2}{x^{2016}+2015}=1+\dfrac{2}{x^{2016}+2015}\le\dfrac{2}{2015}+1=\dfrac{2017}{2015}\)

Dấu '=' xảy ra khi x=0