cho a,b,c thỏa \(\left\{{}\begin{matrix}a,b,c>0\\\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=1\end{matrix}\right.\) chứng minh rằng\(\sqrt{a+bc}+\sqrt{b+ca}+\sqrt{c+ab}\ge\sqrt{abc}+\sqrt{a}+\sqrt{b}+\sqrt{\sqrt{c}}\)

gpt \(\sqrt{2-x}+\sqrt[3]{2x^2+6x+3}=-2\)

gpt a/ \(\left(5x+1\right)\sqrt{2x+1}-\left(7x+3\right)\sqrt{x}=1\)

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

\(\dfrac{\sqrt{x-\sqrt{4\left(x-1\right)}}+\sqrt{x+\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}\left(1-\dfrac{1}{x-1}\right)\) (với \(x>1;x\ne2\))

cho a,b,c,d,e dương CMR \(\dfrac{a}{b+c}+\dfrac{b}{c+d}+\dfrac{c}{d+e}+\dfrac{d}{e+a}+\dfrac{e}{a+b}\ge\dfrac{5}{2}\)

gpt \(8\left(\dfrac{1}{x-2}+\dfrac{1}{x+2}\right)=\dfrac{x^2+4}{x+4}\)

gpt \(\sqrt{x+1}+\sqrt{8-x}+\sqrt{\left(x+1\right)\left(8-x\right)}=3\)