Cho a+b+c =1 TÌm GTNN M= \(\frac{1}{a^2+b^2+c^2}+\frac{1}{abc}\)

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

\(\sqrt{x^2+3x+4}+\sqrt{-y^2+2y+2}=\sqrt{-x^2+5x+14}\)

\(\sqrt{3x^3+2x^2+2}+\sqrt{-3x^3+x^2+2x-1}=2x^2+2x+2\)

Cho a,b,c >0 và \(a^2+b^2+c^2=3\)

\(cmr:\left\{{}\begin{matrix}\dfrac{a}{a^3+2}\le\dfrac{1}{3}\\\dfrac{1}{a^3+2}+\dfrac{1}{b^3+2}+\dfrac{1}{c^3+2}\ge1\end{matrix}\right.\)