Bài 7: Biến đối đơn giản biểu thức chứa căn bậc hai (Tiếp theo)

\(C=\dfrac{\sqrt{x}-\sqrt{y}}{xy\sqrt{xy}}:\left(\dfrac{1}{x}+\dfrac{1}{y}\right).\dfrac{1}{x+y+2\sqrt{xy}}+\dfrac{2}{\left(\sqrt{x}+\sqrt{y}\right)^3}.\left(\dfrac{1}{\sqrt{x}}+\dfrac{1}{\sqrt{y}}\right)\)

a) Rút gọn

b) Tính C với x=2-\(\sqrt{3}\); y=2+\(\sqrt{3}\)

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)

So sánh \(\dfrac{\sqrt{a}-1}{\sqrt{a}}\)với 1

Giải phương trình :

a) \(2\sqrt{x+2}=\sqrt{2x+1}+x\sqrt{x+2}\)

b) \(2+\sqrt{3-8x}=6x+\sqrt{4x-1}\)

c) \(\sqrt{x^2+15}=3x-2+\sqrt{x^2+8}\)

\(\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}+1}-1}\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}+1}-1}\)

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= \(\dfrac{1}{\sqrt{2}-\sqrt{3}}-\dfrac{1}{\sqrt{3}-\sqrt{4}}+\dfrac{1}{\sqrt{4}-\sqrt{5}}-....+\dfrac{1}{\sqrt{100}-\sqrt{101}}\)

M= \(\dfrac{1}{\sqrt{2}-\sqrt{3}}-\dfrac{1}{\sqrt{3}-\sqrt{4}}+\dfrac{1}{\sqrt{4}-\sqrt{5}}-....+\dfrac{1}{\sqrt{100}-\sqrt{101}}\)