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e nghĩ hết cách r mà toàn bị ngược dấu,mấy sư tỉ và sư ca giúp vs

$bài 1:cho: a,b,c>0$$a,t/m:a+b+c=3:CM:\frac{1}{2+a^2+b^2}+\frac{1}{2+b^2+c^2}\frac{1}{2+c^2+a^2}\leq \frac{3}{4}$$b,CM:\frac{\sqrt{ab}}{c+3\sqrt{ab}}+\frac{\sqrt{bc}}{a+3\sqrt{bc}}+\frac{\sqrt{ca}}{b+3\sqrt{ac}}\leq \frac{3}{4}$$c,CM:\frac{1}{(a+b)^2}+\frac{1}{(a+c)^2}\geq \frac{1}{a^2+bc}$$d,CM:\Sigma \frac{1}{a^5+b^2+c^2}\leq \frac{3}{a^2+b^2+c^2}$$e,CM:\Sigma \frac{a+b}{c^2+ab}\leq \frac{1}{b}+\frac{1}{a}+\frac{1}{c}$
Bất đẳng thức Bu-nhi-a-cốp-xki

$bài 1:cho: a,b,c>0$ $a,t/m:a+b+c=3:CM:\frac{1}{2+a^2+b^2}+\frac{1}{2+b^2+c^2}\frac{1}{2+c^2+a^2}\leq \frac{3}{4}$ $b,CM:\frac{\sqrt{ab}}{c+3\sqrt{ab}}+\frac{\sqrt{bc}}{a+3\sqrt{bc}}+\frac{\sqrt{ca}}{b+3\sqrt{ac}}\leq \frac{3}{4}$ $c,CM:\frac{1}{(a+b)^2}+

$bài 1:cho: a,b,c>0$$a,t/m:a+b+c=3:CM:\frac{1}{2+a^2+b^2}+\frac{1}{2+b^2+c^2}\frac{1}{2+c^2+a^2}\leq \frac{3}{4}$$b,CM:\frac{\sqrt{ab}}{c+3\sqrt{ab}}+\frac{\sqrt{bc}}{a+3\sqrt{bc}}+\frac{\sqrt{ca}}{b+3\sqrt{ac}}\leq \frac{3}{4}$$c,CM:\frac{1}{(a+b)^2}+\frac{1}{(a+c)^2}\geq \frac{1}{a^2+bc}$$d,CM:\Sigma \frac{1}{a^5+b^2+c^2}\leq \frac{3}{a^2+b^2+c^2}$$e,CM:\Sigma \frac{a+b}{c^2+ab}\leq \frac{1}{b}+\frac{1}{a}+\frac{1}{c}$
Bất đẳng thức Bu-nhi-a-cốp-xki