Tìm tập xác định của các hàm số sau:

a) y=\(\sqrt{2x-3}\) b) y= \(\sqrt{\left|2x-3\right|}\) c) y= \(\sqrt{4-x}+\sqrt{x+1}\) d) y=\(\sqrt{x-1}+\frac{1}{x-3}\) e) y=\(\frac{1}{\left(x+2\right)\sqrt{x-1}}\)

f) y=\(\sqrt{x+3-2\sqrt{x+2}}\) g) y=\(\frac{\sqrt{5-2x}}{\left(x-2\right)\sqrt{x-1}}\) h) y=\(\sqrt{2x-1}+\sqrt{\frac{1}{3-x}}\) i) y= \(\sqrt{x+3}+\frac{1}{x^2-4}\)

tập xác định hàm số

a, y=\(\sqrt{x^2+x-4}\)

b , y = \(\frac{1}{x^2+1}\)

c , y=\(\frac{\left|2x-3\right|}{x^2+x+6}\)

d , y =\(\frac{1}{x^2-3x}\)

e , y =\(\sqrt{1-x}\) +\(\frac{1}{x\sqrt{1}+x}\)

f , \(\frac{2x-1}{\sqrt{x\sqrt{\left(x-4\right)}}}\)

g, y = \(\frac{x^2+1}{\sqrt{2-5}}\) + \(\frac{1}{x^2-1}\)

h , y= \(\frac{1}{\sqrt{2x^2-4x+4}}\)

i, \(\sqrt{6-x}\)+2x\(\sqrt{2x+1}\)

j, y = \(\sqrt{3+x}\) +\(\frac{1}{x^2-1}\)

k, y = \(\frac{1}{x^2+3x+3}\)+(x+2)\(\sqrt{x+3}\)

l, y =\(\sqrt[3]{\frac{3x+5}{x^2-1}}\)

Tìm tập xác định của các hàm số sau:

a) y = \(\frac{\sqrt{x+1}}{x^2-x-6}\)

b) y = \(\sqrt{6-3x}\) - \(\sqrt{x-1}\)

c) y = \(\frac{\sqrt{2-x}+\sqrt{x+2}}{x}\)

d) y = \(\frac{\sqrt{3x-2}+6x}{\sqrt{4-3x}}\)

e) y = \(\sqrt{6-x}\) + \(\frac{2x+1}{1+\sqrt{x-1}}\)

f) y = \(\frac{2x+9}{\left(x+4\right)\sqrt{x+3}}\)

g) y = \(\frac{\sqrt{x^2-2x+3}}{x-3\sqrt{x}+2}\)

h) f(x) = \(\frac{1}{\sqrt{1-\sqrt{1+4x}}}\)

i) y = \(\frac{2x^2}{\sqrt{x^2-3x+2}}\)

Giải hệ:

\(\left\{{}\begin{matrix}x^2+y^2+xy=5\\27x^3+6y^2x=2+y^3+30x^2y\end{matrix}\right.\)

\(\left\{{}\begin{matrix}x^2+y^2+\frac{8xy}{x+y}=16\\\frac{x^2}{8y}+\frac{2x}{3}=\sqrt{\frac{x^3}{3y}+\frac{x^2}{4}}-\frac{y}{2}\end{matrix}\right.\), \(\left\{{}\begin{matrix}\frac{1}{3x}+\frac{2x}{3y}=\frac{x+\sqrt{y}}{2x^2+y}\\2\left(2x+\sqrt{y}\right)=\sqrt{2x+6}-y\end{matrix}\right.\)

\(\left\{{}\begin{matrix}x^2y-3x-1=3x\sqrt{y}\left(\sqrt{1-x}-1\right)^3\\\sqrt{8x^2-3xy+4y^2}+\sqrt{xy}=4y\end{matrix}\right.\)

Cho các số a,b,c là các số k âm sao cho tổng hai số bất kì đều dương.CMR \(\sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{c+a}}+\sqrt{\frac{c}{a+b}}+\frac{16\sqrt{ab+bc+ac}}{a+b+c}\ge8\)

Giải hpt sau:

a) \(\left\{{}\begin{matrix}\sqrt{5}x+\left(1-\sqrt{3}\right)y=1\\\left(1-\sqrt{3}\right)x+\sqrt{5}y=1\end{matrix}\right.\)

b)\(\left\{{}\begin{matrix}\frac{3x}{x+1}-\frac{2y}{y+4}=4\\\frac{2x}{x+1}-\frac{5y}{y+4}=5\end{matrix}\right.\)

c) \(\left\{{}\begin{matrix}3x-2\left|y\right|=9\\2x+3\left|y\right|=1\end{matrix}\right.\)

d) \(\left\{{}\begin{matrix}\frac{2}{2x-y}+\frac{3}{x-2y}=\frac{1}{2}\\\frac{2}{2x-y}-\frac{1}{x-2y}=\frac{1}{18}\end{matrix}\right.\)