a,b,c>o  a+b+c=3

tìm Max P=a+ab+abc

a,b,c\(\ge\)0

CM \(\dfrac{a^2}{2a^2+bc}+\dfrac{b^2}{2b^2+ca}+\dfrac{c^2}{2c^2+ab}\le1\)

a,b,c>0

a+b+c=3

\(\dfrac{a}{b^3+ab}+\dfrac{b}{a^3+bc}+\dfrac{c}{c^3+ca}\ge\dfrac{3}{2}\)

a,b,c>0

ab+bc+ca=3

CM \(\dfrac{a^2}{a^2+2b}+\dfrac{b^2}{b^2+2c}+\dfrac{c^2}{c^2+2a}\)\(\ge\)1

\(\left\{{}\begin{matrix}4x^3-3x+\left(y-1\right)\sqrt{2y+1}=\dfrac{1}{2}\\2x^2+x+\sqrt{-y\left(2y+1\right)}=0\end{matrix}\right.\)

\(\left\{{}\begin{matrix}x^2+y^2+\dfrac{8xy}{x+y}=16\\2x^2-5x+2\sqrt{x+y}-\sqrt{3x-2}=0\end{matrix}\right.\)

giải hệ phương trình

\(\left\{{}\begin{matrix}\left(y+1\right)^2+y\sqrt{y^2+1}=x+\dfrac{3}{2}\\x+\sqrt{x^2-2x+5}=1+2\sqrt{2x-4y+2}\end{matrix}\right.\)

cho dãy số (u_n):\(\left\{{}\begin{matrix}u_1=2010\\u^2+2019u_n-2011u_{n+1}+1=0\end{matrix}\right.\)

tìm lim\(\left(\Sigma^n_{i=1}\dfrac{1}{u_i+2010}\right)\)

cho dãy số (u_n):\(\left\{{}\begin{matrix}u_1=\sqrt{3}+\sqrt{2}\\u_{n+1}=\left(\sqrt{3}-\sqrt{2}\right)u^2_n+\left(2\sqrt{6}-5\right)u_{n_{ }}+3\sqrt{3}-3\sqrt{2}\end{matrix}\right.\)

tìm lim(\(\Sigma^1_{i=1}\dfrac{1}{u_i+\sqrt{2}}\))

cho dãy số \(\left\{{}\begin{matrix}u_1=2\\u_{n+1}=\dfrac{1}{2}\left(u^2_n+1\right)\end{matrix}\right.\) tìm lim\(\Sigma^n_{i=1}\dfrac{1}{u_i+1}\)