a)ĐKXĐ: \(\left\{{}\begin{matrix}-2x+1\ne0\\\frac{3}{-2x+1}>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{1}{2}\\-2x+1>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{1}{2}\\x< \frac{1}{2}\end{matrix}\right.\)
b) ĐKXĐ: \(x-1\ge0\Leftrightarrow x\ge1\)
c) ĐKXĐ: \(x\in\mathbb{R}\)
Tìm ĐKXĐ
a. \(3-\sqrt{1-16x^2}\)
b. \(\frac{1}{1-\sqrt{x^2-3}}\)
c.\(\sqrt{8x-x^2-15}\)
d. \(\frac{2}{\sqrt{x^2-x+1}}\)
e. \(A=\frac{1}{\sqrt{x-\sqrt{2x-1}}}\)
g. \(\frac{\sqrt{16-x^2}}{\sqrt{2x+1}}+\sqrt{x^2-8x+14}\)
Tìm ĐKXĐ:
a; \(\sqrt[4]{\frac{2}{-7+3x}}\)
b; \(\sqrt{x-1}+\frac{\sqrt[3]{x+1}}{\sqrt{5-x}}\)
c; \(\sqrt[8]{2x-1}-\sqrt[3]{3-5x}\)
d; \(\sqrt{\frac{3x-6-2x}{\sqrt[3]{1-x}}}\)
Tìm ĐKXĐ của các biểu thức :
a/ \(\frac{1}{\sqrt{2x-x^2}}\)
b/ \(\frac{1}{\sqrt{x-3}}+\frac{3x}{\sqrt{5-x}}\)
c/ \(\frac{1}{\sqrt{x^2-5x+6}}\)
d/ \(\sqrt{6x-1}+\sqrt{x+3}\)
Rút gọn biểu thức sau :( chú ý đặt ĐKXĐ trước khi trước khi thực hiện rút gọn)
a,P= \(\frac{3\sqrt{x}+2}{2\sqrt{x}-1}+\frac{\sqrt{x}-1}{\sqrt{x}+4}-\frac{x-6\sqrt{x}+5}{2x+7\sqrt{x}-4}\)
b, D=\(\frac{\sqrt{x}+4}{1-7\sqrt{x}}+\frac{\sqrt{x}-2}{\sqrt{x+1}}+\frac{24\sqrt{x}}{7x+6\sqrt{x}-1}\)
tìm x để các biểu thức sau có nghĩa :
a,\(\sqrt{\frac{4-x}{x+1}}\)
b,\(\sqrt{\frac{2x-3}{3x+1}}\)
c,\(\sqrt{x^2-4}+\sqrt{\frac{x-2}{x+1}}\)
d,\(\sqrt{\frac{x^2-9}{x+1}}\)
e,\(\sqrt{2x-1}+\sqrt{x^3-4x^2-4x+16}\)
f,\(\sqrt{2x-1}-\sqrt{2x^3-11x^2+17x-6}\)
g,\(\frac{1}{\sqrt{x+3}+\sqrt{x^2-1}}\)
Giải phương trình:
a) \(2\sqrt{x^2-4}-3=6\sqrt{x-2}-\sqrt{x+2}\)
b) \(\frac{\sqrt{x-2016}-1}{x-2016}+\frac{\sqrt{y-2017}-1}{y-2017}+\frac{\sqrt{z-2018}-1}{z-2018}=\frac{3}{4}\)
c) \(\sqrt{3+\sqrt{3+x}}=x\)
d) \(\sqrt{6x^2+1}=\sqrt{2x-3}+x^2\)
e) \(\sqrt{x^2+3x+5}+\sqrt{x^2-2x+5}=5\sqrt{x}\)
f) \(\sqrt{x^2+3x}+2\sqrt{x+2}=2x+\sqrt{x+\frac{6}{x}+5}\)
A= \(\frac{x-4\sqrt{x}+2}{\sqrt{x}-2}\) \(\left(x\ge0;x\ne4\right)\)
B= \(\frac{x\sqrt{x}-1}{x-1}\) \(\left(x\ge0;x\ne1\right)\)
C= \(\frac{x\sqrt{x}-1}{x-\sqrt{x}}-\frac{x\sqrt{x}+1}{x+\sqrt{x}}+\frac{x+1}{\sqrt{x}}\) \(\left(x>0;x\ne1\right)\)
D= \(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}\) \(\left(x\ge2\right)\)
E= \(\frac{x+\sqrt{x^2}-2x}{x-\sqrt{x^2-2x}}-\frac{x-\sqrt{x^2-2x}}{x+\sqrt{x^2-2x}}\)
Tìm X để căn thức sau có nghĩa
a) \(\sqrt{1-2x}\) c) \(\sqrt{\frac{4}{5x-3}}\) e)\(\sqrt{1-x^3}\)
b) \(\sqrt{\frac{2}{1-x^2}}\) d) \(\sqrt{\frac{1}{\sqrt[3]{9-x^2}}}\) g) \(\sqrt{4x^2-9}\)
h) \(\sqrt{\frac{5-2x}{x^2+4}}\) i) \(\sqrt[3]{\frac{1-x}{1+x}}\) j) \(\frac{1}{x+\sqrt{x-4}}\)
k) \(\sqrt{\frac{3+x^2}{4-x^2}}\) l) \(\sqrt{\frac{x^2}{1+x}}\)
Tìm điều kiện xác định cho các biểu thức sau:
a) A= 3- \(\sqrt{1-16x^2}\)
b) B= \(\frac{1}{1-\sqrt{x^2-3}}\)
c) C= \(\frac{1}{\sqrt{x-\sqrt{2x-1}}}\)
d) D= \(\sqrt{4x^2-1}\)
e) E= \(\frac{1}{\sqrt{2x-x^2}}\)
f) F= \(\sqrt{x+\frac{3}{x}}\)+ \(\sqrt{-3x}\)
