Tìm x:a, \(\sqrt{x-94}+\sqrt{96-x}=x^2-190x+9027\)
b, \(\sqrt[3]{x-2}+\sqrt{x+1}=3\)
c, \(\dfrac{\sqrt[3]{7-x}-\sqrt[3]{x-5}}{\sqrt[3]{7-x}+\sqrt[3]{x-5}}=6-x\)
Rút gọn biểu thức sau
D = \(\left(\frac{5}{x-\sqrt{x}-6}+\frac{1}{\sqrt{x}+2}\right):\frac{1}{\sqrt{x}-3}\)
E = \(\left(\frac{1}{a-\sqrt{a}}+\frac{1}{\sqrt{a}-1}\right):\frac{\sqrt{a}+1}{a-2\sqrt{a}+1}\)
\(A=\dfrac{\left(\sqrt{a}-\sqrt{b}\right)^2+4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}\)
a) Rút gọn A
b)Cho \(a=\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)và \(b=\sqrt{24}\). Tính A
Rút gọn các biểu thức sau
D = \(\left(\frac{5}{x-\sqrt{x}-6}+\frac{1}{\sqrt{x}+2}\right):\frac{1}{\sqrt{x}-3}\)
E =\(\left(\frac{1}{a-\sqrt{a}}+\frac{1}{\sqrt{a-1}}\right):\frac{\sqrt{a+1}}{a-2\sqrt{a}+1}\)
F = \(\left(\frac{1}{\sqrt{a-1}}+\frac{1}{a-\sqrt{a}}\right):\left(\frac{1}{\sqrt{a}+1}+\frac{2}{a-1}\right)\)
Bài 2 Rút gọn các biểu thức sau
\(A=\frac{\sqrt{x}+4}{\sqrt{x}+1}-\frac{3}{x-1}:\frac{1}{\sqrt{x}-1}\)
B = \(\left(\frac{x-4\sqrt{x}+4}{\sqrt{x}-2}+6\right)\left(\frac{x\sqrt{x}-1}{x+\sqrt{x}+1}-3\right)\)
C = \(\frac{2\sqrt{x}}{x-1}+\frac{1}{x+\sqrt{x}}+\frac{1}{\sqrt{x}-x}\)
Bài 2 Rút gọn các biểu thức sau ( coi các biểu thức đều có nghĩa )
A = \(\frac{\sqrt{x+4}}{\sqrt{x+1}}-\frac{3}{x-1}:\frac{1}{\sqrt{x-1}}\)
B = \(\left(\frac{x-4\sqrt{x+4}}{\sqrt{x-2}}+6\right)\) ( \(\frac{x\sqrt{x}-1}{x+\sqrt{x}+1}-3\) )
C = \(\frac{2\sqrt{x}}{x-1}+\frac{1}{x+\sqrt{x}}+\frac{1}{\sqrt{x}-x}\)
Rút gọn:
\(B=2\sqrt{18}-4\sqrt{32}+\sqrt{72}+3\sqrt{8}\)
\(C=\dfrac{\sqrt{8-2\sqrt{15}}-\sqrt{5}}{\dfrac{1}{\sqrt{3}-2}-\dfrac{1}{\sqrt{3}+2}}\)
Cho số M= 1+\(\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{3}}+..+\dfrac{1}{\sqrt{10^6}}\)
Chứng minh rằng 1998<M<1999
a,\(\dfrac{1}{\sqrt{7-\sqrt{24}+1}}\)-\(\dfrac{1}{\sqrt{7+\sqrt{24}-1}}\)
b,\(\dfrac{1}{3-\sqrt{7}}\)-\(\dfrac{1}{3+\sqrt{7}}\)
c,\(\sqrt{21+6\sqrt{6}}\)+\(\sqrt{21-6\sqrt{6}}\)
