Lời giải:
\(K=\sqrt{4+|1-\sqrt{5}|}.(\sqrt{10}-\sqrt{2})=\sqrt{4+\sqrt{5}-1}.\sqrt{2}(\sqrt{5}-1)\)
\(=\sqrt{3+\sqrt{5}}.\sqrt{2}.(\sqrt{5}-1)=\sqrt{6+2\sqrt{5}}.(\sqrt{5}-1)\)
\(=\sqrt{(\sqrt{5}+1)^2}(\sqrt{5}-1)=(\sqrt{5}+1)(\sqrt{5}-1)=4\)
Chứng minh rằng:
\(\dfrac{1}{3\left(\sqrt{2}+1\right)}+\dfrac{1}{5\left(\sqrt{3}+\sqrt{2}\right)}+\dfrac{1}{7\left(\sqrt{4}+\sqrt{3}\right)}+...+\dfrac{1}{4021\left(\sqrt{2011}+\sqrt{2010}\right)}< \dfrac{1}{2}\left(1-\dfrac{1}{\sqrt{2011}}\right)\)
Rút gọn biểu thức:
A = \(\left(\dfrac{\sqrt{x}+1}{\sqrt{xy}+1}+\dfrac{\sqrt{xy}+\sqrt{x}}{1-\sqrt{xy}}+1\right):\left(1-\dfrac{\sqrt{xy}+\sqrt{x}}{\sqrt{xy}-1}-\dfrac{\sqrt{x}+1}{\sqrt{xy}+1}\right)\)
Giúp mk làm bài này với ạ!!!
thực hiện phép tính
a, \(\dfrac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
b, \(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
c, \(\sqrt{2-\sqrt{3}}.\left(\sqrt{5}+\sqrt{2}\right)\)
d, \(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
e, \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
f, \(\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}\)
g, \(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
h, \(\dfrac{6+4\sqrt{2}}{\sqrt{2}+\sqrt{6+4\sqrt{2}}}+\dfrac{6-4\sqrt{2}}{\sqrt{2}+\sqrt{6+4\sqrt{2}}}\)
i, \(\dfrac{\left(\sqrt{5+2}\right)^2-8\sqrt{5}}{2\sqrt{5}-4}\)
k, \(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)
l, \(\dfrac{4}{\sqrt{3}+1}+\dfrac{1}{\sqrt{3}-2}+\dfrac{6}{\sqrt{3}-3}\)
m, \(\left(\sqrt{2}+1\right)^3-\left(\sqrt{2}-1\right)^3\)
n, \(\dfrac{\sqrt{3}}{1-\sqrt{\sqrt{3+1}}}+\dfrac{\sqrt{3}}{1+\sqrt{\sqrt{3+1}}}\)
\(\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)
Cho \(x=\dfrac{1}{\sqrt[3]{3-2\sqrt{2}}}+\sqrt[3]{3-2\sqrt{2}}\)
Tính \(P=\left(2x^3-6x+2008\right)^{2020}\)
Giúp với ạ
Giải hệ phương trình:
\(\left\{{}\begin{matrix}2\left(\dfrac{x^3}{y^2}+\dfrac{y^3}{x^2}\right)=\sqrt[4]{8\left(x^4+y^4\right)}+2\sqrt{xy}\\16x^5-20x^3+5\sqrt{xy}=\sqrt{\dfrac{y+1}{2}}\end{matrix}\right.\)
Mình đang cần gấp lắm, các bạn giúp mình với. Cảm ơn!
thực hiện phép tính:\(\sqrt{\left(5-\sqrt{24}^{ }\right)^2}\)- \(\sqrt{\left(5+\sqrt{24}\right)^2}\)
\(\left\{\dfrac{\sqrt{x}-1}{3\sqrt{x}-1}-\dfrac{1}{3\sqrt{x}+1}+\dfrac{8\sqrt{x}}{9x-1}\right\}:\left\{1-\dfrac{3\sqrt{x}-2}{3\sqrt{x}+1}\right\}\)
a, Rút gọn P
b, Tìm các giá trị của x để P = \(\dfrac{6}{5}\)
Giúp mình với ạ, Cảm ơn trước!
\(\dfrac{\sqrt{x}}{\sqrt{x}-1}-\dfrac{6\sqrt{x}-3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
Rút gọn ạ
