ĐKXĐ:\(x-2\ge0\Rightarrow x\ge2\)
\(\sqrt{x-2}=3\\ \Leftrightarrow\sqrt{\left(x-2\right)^2}=3^2\\ \Leftrightarrow x-2=9\\ \Leftrightarrow x=11\left(tm\right)\)
Gidipt 1) sqrt(x ^ 2 - x) = sqrt(3 - x)
2) sqrt(x ^ 2 - 4x + 3) = x - 2
3) sqrt(4 * (1 - x) ^ 2) - 6 = 0
4) sqrt(x ^ 2 - 4x + 4) = sqrt(4x ^ 2 - 12x + 9)
5) sqrt(x ^ 2 - 4) + sqrt(x ^ 2 + 4x + 4) = 0
6) 1sqrt(x + 2sqrt(x - 1)) + sqrt(x - 2sqrt(x - 1)) = 2
1: rút gọn \(A=\dfrac{2}{x^2-1}-\dfrac{1}{x^2+x}+\dfrac{x^2-3}{x^3-x}\); \(B=\dfrac{2}{x-1}+\dfrac{2x-1}{x^2+x+1}+\dfrac{x^2+6x+2}{x^3-1}\)
2: tìm x: \(\dfrac{4}{3}\left(x-2\right)+\dfrac{\left(x-1\right)\left(x+2\right)}{2}=3-\dfrac{5x\left(1-2x\right)}{4}\)
rút gọn biểu thức
a) A= \(2\sqrt{\frac{1}{2}}+\sqrt{18}\)
b) B= \(\frac{5+3\sqrt{5}}{\sqrt{5}}+\frac{3+\sqrt{3}}{\sqrt{3}+1}-\left(\sqrt{5+3}\right)\)
c) C= \(\frac{1}{x+\sqrt{x}}+\frac{2\sqrt{x}}{x-1}-\frac{1}{x-\sqrt{x}}\left(x>0,x\ne1\right)\)
d) D = \(\left(\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}-\frac{\sqrt{x-2}}{x-1}\right)\left(x+\sqrt{x}\right)\left(x>0,x\ne1\right)\)
e) E = \(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
d) \(\sqrt{x^2-12x+36}-x=3\)
e) \(\sqrt{x^2-4x+5}-1=x\)
f) \(\sqrt{x^2-6x+9}+x=3\)
h) \(\sqrt{18x}+\sqrt{32x}-14=0\)
k) \(\sqrt{6x-3}+2=\sqrt{3}\)
1.\(\sqrt{-4x^2+25}=x\)
2.\(\sqrt{3x^2-4x+3}=1-2x\)
3. \(\sqrt{4\left(1-x\right)^2}-\sqrt{3}=0\)
4.\(\dfrac{3\sqrt{x+5}}{\sqrt{ }x-1}< 0\)
5. \(\dfrac{3\sqrt{x-5}}{\sqrt{x+1}}\ge0\)
Mong mng giúp ạ
câu1 rút gọn
a)\(\sqrt{4-2\sqrt{3}}-\sqrt{3}\)
b)\(\dfrac{x^2+2\sqrt{2}x+2}{x^2-2}\left(x\ne\sqrt{2},x\ne-\sqrt{2}\right)\)
c)\(\sqrt{9\text{x}^2}-2\text{x}\left(x< 0\right)\)
d)\(\sqrt{11+6\sqrt{2}}-3+\sqrt{2}\)
e)\(\dfrac{x^2-5}{x+\sqrt{5}}\left(x\ne-\sqrt{5}\right)\)
√x^2-6x+9=3-x
x^2-1/2x+1/16=x+3/2
√x-2√x-1=√x-1-1
√9-4√5-√5=-2
\(\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}\right)\)
Bài 1: Tìm GTLN và GTNN
A= (√x - 1)2 - 3√x + 7
B= (√x + 2)2- 5√x - 7
C= (√x+ 1)2 - 3√5 - 12
D= 7√x - (√x - 2)2 + 3
E= 3√x - (√x - 3)2 - 12
`(x+1)/5=(x+2)/4=(x+3)/3+(x+2)/4`
