Ruffer

Mình giải như sau

Ta có:

$\sqrt{2a-1}\leq \frac{2a-1+1}{2}=a\rightarrow \frac{\sqrt{2a-1}}{a}\leq 1$$\sqrt{2a-1}\leq \frac{2a-1+1}{2}=a\rightarrow \frac{\sqrt{2a-1}}{a}\leq 1$

$\sqrt[3]{3b-2}\leq \frac{3b-2+1+1}{3}=b\rightarrow \frac{\sqrt[3]{3b-2}}{b}\leq 1$

$\sqrt[4]{4c-3}\leq \frac{4c-3+1+1+1}{4}=c\rightarrow \frac{\sqrt[4]{4c-3}}{4}\leq 1$

1.cho 0<a,b,c<\frac{1}{3}  

$a^{2}+b^{2}+c^{2}=\frac{3}{64}$

cmr P=$\frac{1}{1-3a}+\frac{1}{1-3b}+\frac{1}{1-3c}\geq 12$

$\frac{\sqrt{2a-1}}{a}+\frac{\sqrt[3]{3b-2}}{b}+\frac{\sqrt[4]{4c-3}}{c}\leq 3$

cho a,b,c>0 a+b+c=1 $\sqrt[3]{ab}+\sqrt[3]{cb}+\sqrt[3]{ac}\leq \sqrt[3]{3}$

cái bài này hình như nhân $\frac{1}{\sqrt[3]{3}}$ rồi áp dụng bdt cô si nhưng mình quên mất lm tn

cho a,b,c >1 cmr $\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}\geq \frac{3}{1+\sqrt[3]{abc}}$

tìm min max $P=\frac{4\sqrt{5xy-16^2}}{x^2 +(4y)^2}$ x khác 0

a,b,c>0 tìm min  $M=a\sqrt{3b(a+2b)}+b\sqrt{3a(b+2a)}$