\(\left(\frac{\sqrt{8}}{3}\right)^2=\frac{8}{9}>\frac{9}{16}=\left(\frac{3}{4}\right)^2\Rightarrow\frac{\sqrt{8}}{3}>\frac{3}{4}\)
\(sosanh\frac{-\sqrt{10}}{2}va-2\sqrt{5}\)
a,Cho a,b,c duong va \(a^2+b^2+c^2\)=3. Tim Min cua P= \(\frac{a^3}{\sqrt{b^2+3}}+\frac{b^3}{\sqrt{c^2+3}}+\frac{c^3}{\sqrt{a^2+3}}\)
b,Cho x,y,z>0 va x+y+z=6. C/m \(8^x+8^y+8^z\ge4^{x+1}+4^{y+1}+4^{z+1}\)
So sánh:
1,\(2-\sqrt{2}va\frac{1}{2}\)
2, \(2\sqrt{3}-5va\sqrt{3}-4\)
3, \(\sqrt{3}-3\sqrt{2}va-4\sqrt{3}+5\sqrt{2}\)
4,\(1-\sqrt{3}va\sqrt{2}-\sqrt{6}\)
5, \(\sqrt{4\sqrt{5}}va\sqrt{5\sqrt{3}}\)
6, \(\sqrt{\sqrt{6}-\sqrt{5}}-\sqrt{\sqrt{3}-\sqrt{2}}va..0\)
7, \(-2\sqrt{\frac{1}{2}\sqrt{5}}va-3\sqrt{\frac{1}{3}\sqrt{2}}\)
\(\frac{3}{\sqrt{4}+\sqrt{8}}+\frac{3}{\sqrt{8}+\sqrt{12}}+\frac{3}{\sqrt{12}+\sqrt{16}}+...+\frac{3}{\sqrt{572}+\sqrt{576}}.\)
\(\sqrt[3]{\frac{1}{4}+\frac{\sqrt{5}}{8}}-\sqrt[3]{\frac{\sqrt{5}}{8}-\frac{1}{4}}=\)
\(\frac{1}{\sqrt{1}-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-\frac{1}{\sqrt{4}-\sqrt{5}}+\frac{1}{\sqrt{5}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{9}}\)
RUT GON
Rút gọn : \(\frac{1}{\sqrt{1}-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-\frac{1}{\sqrt{4}-\sqrt{5}}+\frac{1}{\sqrt{5}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{9}}\)
Tính:
a/ \(\frac{3+\sqrt{5}}{\sqrt{2}+\sqrt{3+\sqrt{5}}}+\frac{3-\sqrt{5}}{\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
b/ \(\frac{\sqrt{20+8\sqrt{3}}+\sqrt{20-8\sqrt{3}}}{\sqrt{5+2\sqrt{3}}-\sqrt{5-2\sqrt{3}}}-\frac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\$\sqrt{4+\sqrt{3}}-\sqrt{4-\sqrt{3}}}\)
tính tổng:
\(\frac{\sqrt{3}}{\sqrt[3]{2}+\sqrt[3]{4}}+\frac{\sqrt{5}}{\sqrt[3]{4}+\sqrt[3]{6}}+\frac{\sqrt{7}}{\sqrt[3]{6}+\sqrt[3]{8}}+...+\frac{\sqrt{57}}{\sqrt[3]{56}+\sqrt[3]{58}}+\frac{\sqrt{59}}{\sqrt[3]{58}+\sqrt[3]{60}}\)