\(\left(1-\dfrac{3-\sqrt{3}}{\sqrt{3}-1}\right)\left(\dfrac{3+\sqrt{3}}{\sqrt{3}+1}-1\right)\)
= \(\dfrac{-3+\sqrt{3}+\sqrt{3}-1}{\sqrt{3}-1}.\dfrac{3+\sqrt{3}-\sqrt{3}-1}{\sqrt{3}+1}\)
= \(\dfrac{2\sqrt{3}-4}{\sqrt{3}-1}.\dfrac{2}{\sqrt{3}+1}\) = \(\dfrac{4\sqrt{3}-8}{2}\) = \(2\sqrt{3}-4\)
Bài 1 Rút gọn biểu thức:
a) \(\dfrac{\sqrt{3-\sqrt{5}.}\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
b) \(\dfrac{4}{\sqrt{3}+1}+\dfrac{1}{\sqrt{3}-1}+\dfrac{6}{\sqrt{3}-3}\)
A = \(\dfrac{4+\sqrt{3}}{\sqrt{1}+\sqrt{3}}+\dfrac{6+\sqrt{8}}{\sqrt{3}+\sqrt{5}}+...+\dfrac{2n+\sqrt{n^2-1}}{\sqrt{n-1}+\sqrt{n+1}}+\dfrac{240+\sqrt{14399}}{\sqrt{119}+\sqrt{121}}\)
B= \(\dfrac{1}{\sqrt{2}-\sqrt{3}}-\dfrac{1}{\sqrt{3}-\sqrt{4}}+\dfrac{1}{\sqrt{4}-\sqrt{5}}-....+\dfrac{1}{\sqrt{100}-\sqrt{101}}\)
1. \(\dfrac{-2}{\sqrt{3}-1}\)
2. \(\dfrac{5}{1-\sqrt{6}}\)
3. \(\dfrac{2+\sqrt{5}}{2-\sqrt{5}}\)
4. \(\dfrac{1}{5+2\sqrt{6}}\)
5. \(\dfrac{\sqrt{5}+2}{\sqrt{5}-2}\)
6. \(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{2}-\sqrt{5}}\)
7. \(\dfrac{\sqrt{20}-3\sqrt{10}}{3-\sqrt{2}}\)
8. \(\dfrac{6-2\sqrt{5}}{3+\sqrt{5}}\)
9. \(\dfrac{9+4\sqrt{5}}{\sqrt{5}+2}\)
Rút gọn
\(A=\dfrac{1+\sqrt{5}}{\sqrt{2}+\sqrt{3+\sqrt{5}}}+\dfrac{1-\sqrt{5}}{\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
\(B=\dfrac{1}{\sqrt{1}-\sqrt{2}}+\dfrac{1}{\sqrt{2}-\sqrt{3}}+....+\dfrac{1}{\sqrt{n-1}-\sqrt{n}}\) (n thuộc N, n>=2)
Tính:
a, A= \(\sqrt{\dfrac{3+\sqrt{5}}{3-\sqrt{5}}}\)+ \(\sqrt{\dfrac{3-\sqrt{5}}{3+\sqrt{5}}}\)
b, B= \(\dfrac{3+\sqrt{5}}{2\sqrt{2}+\sqrt{3+\sqrt{5}}}\)+ \(\dfrac{3-\sqrt{5}}{2\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
c, C= \(\dfrac{1}{2\sqrt{1}+1\sqrt{2}}+\dfrac{1}{3\sqrt{2}+2\sqrt{3}}+...+\dfrac{1}{25\sqrt{24}+24\sqrt{25}}\)
Bài 1: Tính:
\(\dfrac{1}{\sqrt{3}}+\dfrac{1}{3\sqrt{2}}+\dfrac{1}{\sqrt{3}}\sqrt{\dfrac{5}{12}-\dfrac{1}{\sqrt{6}}}\)
Bài 2: Rút gọn rồi tính:
a) A=\(\dfrac{a^4-4a^2+3}{a^4-12a^2+27},a=\sqrt{3}-\sqrt{2}\)
b) \(B=\dfrac{1}{\sqrt{h+2\sqrt{h-1}}}+\dfrac{1}{\sqrt{h-2\sqrt{h-1}}},h=3\)
c) \(C=\dfrac{\sqrt{2x+2\sqrt{x^2-4}}}{\sqrt{x^2-4}x+2},x=2\left(\sqrt{3}+1\right)\)
d) \(D=\left(\dfrac{3}{\sqrt{1+a}}+\sqrt{1-a}\right):\left(\dfrac{3}{\sqrt{1-a^2}}+1\right),a=\dfrac{\sqrt{3}}{2+\sqrt{3}}\)
Mọi người giúp em với!!!!!!!!!!!!!!
Rút gọn các biểu thức :
a) \(\dfrac{2}{\sqrt{3}-1}-\dfrac{2}{\sqrt{3}+1}\)
b) \(\dfrac{5}{12\left(2\sqrt{5}+3\sqrt{2}\right)}-\dfrac{5}{12\left(2\sqrt{5}-3\sqrt{2}\right)}\)
c) \(\dfrac{5+\sqrt{5}}{5-\sqrt{5}}+\dfrac{5-\sqrt{5}}{5+\sqrt{5}}\)
d) \(\dfrac{\sqrt{3}}{\sqrt{\sqrt{3+1}}-1}-\dfrac{\sqrt{3}}{\sqrt{\sqrt{3+1}}+1}\)
\(\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}+1-1}}-\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}}+1+1}\)
\(\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}+1}-1}-\dfrac{\sqrt{3}}{\sqrt{\sqrt{3+1}+1}}\)
