Rút gọn :

M = \(\frac{1}{3.\left(\sqrt{1}+\sqrt{2}\right)}+\frac{1}{5.\left(\sqrt{2}+\sqrt{3}\right)}+\frac{1}{7.\left(\sqrt{3}+\sqrt{4}\right)}+....+\frac{1}{49.\left(\sqrt{24}+\sqrt{25}\right)}\)

Rút gọn:

a. \(\sqrt{7+2\sqrt{17\sqrt{2}}}-\sqrt{3\sqrt{2}+1}\)

b. \(\frac{\sqrt{20+8\sqrt{3}}+\sqrt{20-8\sqrt{3}}}{\sqrt{5+2\sqrt{3}}-\sqrt{5-2\sqrt{3}}}\) - \(\frac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{3}}-\sqrt{4-\sqrt{3}}}\)

Rút gọn:

a. \(\sqrt{6+\sqrt{24}+\sqrt{12}+\sqrt{8}}-\sqrt{4-2\sqrt{3}}\)

b.\(\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right).\left(\sqrt{6}+11\right)\)

Gpt:

a. \(13\sqrt{x-1}+9\sqrt{x+1}\) = 16x

b. \(x^4+\sqrt{x^2+43}=43\)

CM : \(\frac{1}{2\sqrt{1}}+\frac{1}{3\sqrt{2}}+\frac{1}{4\sqrt{3}}+......\frac{1}{\left(n+1\right)\sqrt{n}}\) < 2

So sánh :

\(\frac{2009}{\sqrt{2011}}+\frac{2011}{\sqrt{2009}}\) và \(\sqrt{2009}+\sqrt{2011}\)

Cho x= \(\frac{\sqrt{5}-1}{2}\) Tính : A = \(\frac{\left(x^2+x-3\right)^{2015}}{\left(x^5+x^4-x^3-2\right)^{2015}}\) + ( x⁵ + x⁴ -x³ -2 )²⁰¹⁵

Rút gọn ;

a. \(\sqrt{49-5\sqrt{96}}+\sqrt{49+5\sqrt{96}}\)

b. ( 3\(\sqrt{2}+\sqrt{10}\) ).\(\sqrt{38-12\sqrt{5}}\)

Cho tam giác ABC cân tại C có AB=\(\sqrt{32}\) . Đường trung tuyến AD . CM diện tích tam giác ABC =5 . Tính độ dài cạnh bên