\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}×\sqrt{2004-2\sqrt{2006}-2\sqrt{2005}}=\sqrt{2004-2\sqrt{2006-2\sqrt{2005}}}\)
\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}×\sqrt{2004-2\sqrt{2006}-2\sqrt{2005}}=\sqrt{2004-2\sqrt{2006-2\sqrt{2005}}}\)
1/ So sánh
a) 3 - 2\(\sqrt{3}\) và 2\(\sqrt{6}\) - 5
b) \(\sqrt{4\sqrt{5}}\) và \(\sqrt{5\sqrt{3}}\)
c) 3 - 2\(\sqrt{5}\) và 1 - \(\sqrt{5}\)
d) \(\sqrt{2006}\) - \(\sqrt{2005}\) và \(\sqrt{2005}\) - \(\sqrt{2004}\)
e) \(\sqrt{2003}\) + \(\sqrt{2005}\) và \(2\sqrt{2004}\)
2/ Tìm giá trị nhỏ nhất hoặc giá trị lớn nhất
a) -x² + 4x - 2
b) \(\sqrt{2x^2\:+\:3}\)
c) 2x - \(\sqrt{1x}\)
d) -3 + \(\sqrt{2x^2\:+\:49}\)
e) \(\sqrt{9x^2\:-\:4x\:+\:65}\)
f) -5 + \(\sqrt{4\:-\:9x^2\:+\:6x}\)
So sánh:
a) \(\sqrt{3}+\sqrt{5}\) và \(\sqrt{17}\)
b) \(\sqrt{2004}+\sqrt{2006}\)và \(2\sqrt{2005}\)
So sánh : a, \(\sqrt{3}+\sqrt{5}với\sqrt{17}\)
b,\(\sqrt{2004}+\sqrt{2006}với2\sqrt{2005}\)
a) A=\(\sqrt{\left(4-\sqrt{15}\right)^2+\sqrt{15}}\)
b) B=\(\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(1-\sqrt{3}\right)^2}\)
c) C=\(\sqrt{49-12\sqrt{5}}-\sqrt{49+12\sqrt{5}}\)
d)D=\(\sqrt{29+12\sqrt{5}-\sqrt{29-12\sqrt{5}}}\)
\(\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}=\sqrt{5}-\sqrt{3\sqrt{\left(\sqrt{20-3}\right)^2}}\)
\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-6\sqrt{20}}}}\)
\(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)
Mấy bạn giúp mình với nhé
1. Rút gọn các biểu thức sau
a. \(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+......+\frac{1}{\sqrt{2004}+\sqrt{2005}}\)
b. \(\frac{\sqrt{2+\sqrt{3}}}{2.\left(\sqrt{2}+\sqrt{6}\right)}\) c. \(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)\) d. \(\sqrt{5-\sqrt{3}}-\sqrt{5+\sqrt{3}}\)
e. \(\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}\) f. \(\sqrt{5+\sqrt{21}}.\left(\sqrt{6}-\sqrt{14}\right)\)
g.\(\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right).\left(\sqrt{10}+\sqrt{2}\right)\) h. \(\frac{\sqrt{3+\sqrt{5}}.\left(\sqrt{5}-1\right)}{2\sqrt{2}}\)
i. \(\sqrt{5-\sqrt{3-\sqrt{29-6\sqrt{20}}}}\) k. \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{9-12\sqrt{5}}}}\)
Chứng tỏ rằng
\(\frac{2}{3\left(1+\sqrt{2}\right)}+\frac{2}{5\left(\sqrt{2}+\sqrt{3}\right)}+\frac{2}{7\left(\sqrt{3}+\sqrt{4}\right)}+...+\frac{2}{4011\left(\sqrt{2005}+\sqrt{2006}\right)}<1-\frac{1}{\sqrt{2006}}\)
so sánh \(\sqrt{2006}-\sqrt{2005}\)và\(\sqrt{2005}-\sqrt{2004}\)
Chứng tỏ rằng
\(\frac{2}{3\left(1+\sqrt{2}\right)}+\frac{2}{5\left(\sqrt{2}+\sqrt{3}\right)}+\frac{2}{7\left(\sqrt{3}+\sqrt{4}\right)}+...+\frac{2}{4011\left(\sqrt{2005}+\sqrt{2006}\right)}<1-\frac{1}{\sqrt{2006}}\)