Cho \(a,b,c>0\). Tìm Min \(Q=\frac{a^2}{a^2+\left(b+c\right)^2}+\frac{b^2}{b^2+\left(c+a\right)^2}+\frac{c^2}{c^2+\left(a+b\right)^2}\)

1. cho \(0< a\le b\le c\) . Cmr: \(\frac{2a^2}{b^2+c^2}+\frac{2b^2}{c^2+a^2}+\frac{2c^2}{a^2+b^2}\le\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\)

2. cho \(a,b,c\ge0\). cmr: \(a^2+b^2+c^2+3\sqrt[3]{\left(abc\right)^2}\ge2\left(ab+bc+ca\right)\)

3. \(a,b,c>0.\) Cmr: \(\sqrt{\left(a^2b+b^2c+c^2a\right)\left(ab^2+bc^2+ca^2\right)}\ge abc+\sqrt[3]{\left(a^3+abc\right)\left(b^3+abc\right)\left(c^3+abc\right)}\)

4. \(a,b,c>0\). Tìm Min \(P=\left(\frac{a}{a+b}\right)^4+\left(\frac{b}{b+c}\right)^4+\left(\frac{c}{c+a}\right)^4\)

Cho \(\left\{{}\begin{matrix}x,y,z< 1\\x^3+y^3+z^3=\frac{3}{2\sqrt{2}}\end{matrix}\right.\) Tìm Min \(A=\frac{x^2}{\sqrt{1-x^2}}+\frac{y^2}{\sqrt{1-y^2}}+\frac{z^2}{\sqrt{1-z^2}}\)

3,8 : (x+1,05) = 19/27

x+1,05=3,8:19/27

x+1,05=5,4

x=5,4-1,05

x=4,35