\(n\ge3;a,b,c>0\)

CMR :

\(\dfrac{1}{a^n\left(b+c\right)}+\dfrac{1}{b^n\left(c+a\right)}+\dfrac{1}{c^n\left(a+b\right)}\ge\dfrac{3}{2}\)

Akai Haruma

a+b+c = 4 ; a,b,c >0

Tìm GTNN của :

\(\frac{a^4}{\left(a+b\right)\left(a^2+b^2\right)}+\frac{b^4}{\left(b+c\right)\left(b^2+c^2\right)}+\frac{c^4}{\left(c+a\right)\left(c^2+a^2\right)}\)

ab + bc + ca = 3 ; a,b,c >0 CMR:

\(\frac{a}{a^2+7}+\frac{b}{b^2+7}+\frac{c}{c^2+7}\le\frac{3}{8} \)

\(x^2+y^2+z^2=2\)

Tìm GTLN và GTNN của :

\(P=\dfrac{x}{2+yz}+\dfrac{y}{2+zx}+\dfrac{z}{2+xy}\)

\(x^2+y^2+z^2=2\)

\(x+y+z\le xy+2\)

5x9+7

=45+7

=52