\(a.\Leftrightarrow2x+1>7^2\)
\(\Leftrightarrow2x+1>49\)
\(\Leftrightarrow x>24\)
\(b.\Leftrightarrow2x-1\le\left(\dfrac{3}{2}\right)^2\\ \Leftrightarrow2x-1\le\dfrac{9}{4}\\ \Leftrightarrow2x\le\dfrac{13}{4}\\ \Leftrightarrow x\le\dfrac{13}{8}\)
\(\sqrt{\dfrac{x+2}{4}}+\sqrt{25x+50}-2\sqrt{x+2}=14\) ; \(\sqrt{2x+3}=x\) ; \(\sqrt{25x^2+20x+4}=1\) ; \(\sqrt{\dfrac{x+1}{2x-1}}=2\) ; \(\dfrac{\sqrt{x-2}}{\sqrt{3x+1}}=6\)
Tìm x
Rút gọn các biểu thức sau
a,\(A=\left(\dfrac{1}{x-\sqrt{x}}+\dfrac{1}{\sqrt{x}-1}\right):\dfrac{\sqrt{x}+1}{x-2\sqrt{x}+1}\)
b,\(B=\dfrac{2\sqrt{x}-1}{\sqrt{x}+1}+\dfrac{3\sqrt{x}-1}{x-\sqrt{x}+1}-\dfrac{2x\sqrt{x}-2x+2\sqrt{x}-3}{x\sqrt{x}+1}\)
c,\(C=\left(1-\dfrac{x+3\sqrt{x}}{x-9}\right):\left(\dfrac{\sqrt{x}-3}{2-\sqrt{x}}+\dfrac{\sqrt{x}-2}{3+\sqrt{x}}-\dfrac{9-x}{x+\sqrt{x}-6}\right)\)
d,\(D=\left(\dfrac{\sqrt{x}}{3+\sqrt{x}}+\dfrac{x+9}{9-x}\right):\left(\dfrac{3\sqrt{x}+1}{x-3\sqrt{x}}-\dfrac{1}{\sqrt{x}}\right)\)
e,\(E=\dfrac{15\sqrt{x}-11}{x+2\sqrt{x}-3}+\dfrac{3\sqrt{x}-2}{1-\sqrt{x}}-\dfrac{2\sqrt{x}+3}{\sqrt{x}+3}\)
1. Tính:
\(\sqrt{\dfrac{x-1+\sqrt{2x-3}}{x+2-\sqrt{2x+3}}}\)
2. Chứng minh:
a) \(\dfrac{\left(3\sqrt{xy}-6y.2x\sqrt{y}+4y\sqrt{x}\right)\left(3\sqrt{y}+2\sqrt{xy}\right)}{y\left(\sqrt{x}-2\sqrt{y}\right)\left(y-4x\right)}=1\)
b) \(\left(\sqrt{x}-\sqrt{y}-\dfrac{\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\right)\left(\dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{y}}+\dfrac{y}{\sqrt{x}-\sqrt{y}}-\dfrac{2\sqrt{xy}}{xy}\right)=\sqrt{x}+\sqrt{y}\)
\(\sqrt{2x+11}+\sqrt{x-1}\) ; \(\dfrac{\sqrt{-5x}}{x}\) ; \(\dfrac{\sqrt{7x^2+1}}{5}\); \(\sqrt{x^2-14x+33}\); \(\dfrac{\sqrt{-x^2+6x+16}}{-2}+\dfrac{x^2-2x}{3x^2}\)
Tìm ĐKXĐ của x để các biểu thức trên có nghĩa
tìm x:
\(\sqrt{x^2+x+1}=1\)
\(\sqrt{x^2+1}=-3\)
\(\sqrt{x^2-10x+25}=7-2x\)
\(\sqrt{2x+5}=5\)
\(\sqrt{x^2-4x+4}-2x+5=0\)
rút gọn biểu thức
e) \(\dfrac{\sqrt{a}-a}{\sqrt{a}-1}\)
f)\(\dfrac{\sqrt{7-4\sqrt{3}}}{\sqrt{3}-2}\)
2) giải phương trình
a)\(\sqrt{\dfrac{2x-3}{x-1}=2}\)
b)\(\dfrac{\sqrt{2x-3}}{\sqrt{x-1}}=2\)
ai giúp e mấy câu này với ạ !!!
\(\sqrt{x^2-\dfrac{1}{4}+\sqrt{x^2+x+\dfrac{1}{4}}=\dfrac{1}{2}\left(2x^3+x^2+2x+1\right)}\)
Cho \(A=\left(\dfrac{2}{\sqrt{x}-2}+\dfrac{3}{2\sqrt{x}+1}-\dfrac{5\sqrt{x}7}{2x-3\sqrt{2}-2}\right):\dfrac{2\sqrt{x}+3}{5x-10\sqrt{x}}\)
a. Rut gon A voi \(x>0,x\ne4\)
b. Tim x de A nguyen
Tìm x để các biểu thức sau có nghĩa:
1) \(\sqrt{-2x}\)
2) \(\sqrt{15x}\)
3) \(\sqrt{2x+1}\)
4) \(\sqrt{3-6x}\)
5) \(\dfrac{1}{2-\sqrt{x}}\)
6) \(\dfrac{3}{\sqrt{x^2-1}}\)
7) \(\sqrt{2x^2+3}\)
8) \(\dfrac{5}{\sqrt{-x^2-2}}\)
Bài 1 : Tìm điều kiện xác định của các biểu thức sau:
a, \(\sqrt{\dfrac{-5}{x^2+6}}\) g,\(\sqrt{2x^2-5X}+3\)
b. \(\sqrt{\left(x-1\right)\left(x-3\right)}\) h, \(\dfrac{1}{\sqrt{x^2-5x+6}}\)
c. \(\sqrt{x^2-4}\) k, \(\dfrac{1}{\sqrt{x-3}}+\dfrac{3x}{\sqrt{5-x}}\)
d.\(\sqrt{\dfrac{2-x}{x+3}}\) m,\(\dfrac{1}{\sqrt{2x-x^2}}\)
e.\(\sqrt{x^2-3x}+7\) n, \(\sqrt{6x-1}+\sqrt{x+3}\)
