c) \(\sqrt{\left(x-2\right)^2}=x+2\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}-2\le x< 2\\-\left(x-2\right)=x+2\Rightarrow2x=0\Rightarrow x=0\end{matrix}\right.\\\left\{{}\begin{matrix}2\le x\\\left(x-2\right)=x+2\Rightarrow-2=2\Rightarrow voN_0\end{matrix}\right.\end{matrix}\right.\)
x=0 duy nhat
Tìm x bt:
\(\sqrt{x^2+2x+1}\) = -x
Rút gọn:
a, \(\sqrt{\left(4-\sqrt{17}\right)}^2\) - \(\sqrt{17}\)
b, \(\sqrt{\left(5-2\sqrt{3}\right)^2}\) - \(2\sqrt{3}\)
a. \(\sqrt{x}\left(\sqrt{x}-3\right)-5\left(\sqrt{x}+3\right)\)
b. \(3\left(2+\sqrt{x}\right)+\left(\sqrt{x}+3\right)\left(2-\sqrt{x}\right)\)
c. \(\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)-5\left(\sqrt{x}-1\right)\)
d. \(3\left(\sqrt{x}-2\right)-\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
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) \(\left(\sqrt{x}-\sqrt{y}-\dfrac{\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\right)\left(\dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{y}}+\dfrac{y}{\sqrt{x}-\sqrt{y}}-\dfrac{2\sqrt{xy}}{xy}\right)=\sqrt{x}+\sqrt{y}\)
Giải các pt sau:
1, \(\sqrt{x^2+x+1}=2x+\sqrt{x^2-x+1}\)
2, \(2x^2+2x+6=2x\sqrt{x^2-x+1}+4\sqrt{3x+1}\)
3, \(\left(\sqrt{x+3}-\sqrt{x}\right)\left(1+\sqrt{x^2+3x}\right)=3\)
4, \(\sqrt{2x^2-1}+\sqrt{x^2-3x-2}=\sqrt{2x^2-2x+3}+\sqrt{x^2-x+2}\)
5, \(13\sqrt{x-1}+9\sqrt{x+1}=16x\)
1. Rút gọn \(A=\sqrt{x+\sqrt{2x-1}}-\sqrt{x-\sqrt{2x-1}}\)
2. Tính \(B=\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}}\)
3.Tính \(C=\frac{\sqrt{3-\sqrt{5}}\cdot\left(\sqrt{10}-\sqrt{2}\right)\cdot\left(3+\sqrt{5}\right)}{\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}}\)
Rút Gọn
a) A = \(\dfrac{1}{\sqrt{x}+\sqrt{x-1}}\) \(-\)\(\dfrac{1}{\sqrt{x}-\sqrt{x-1}}\)\(-\)\(\dfrac{x\sqrt{x}-x}{1-\sqrt{x}}\)( Rút gọn và Tìm x để A > 0 )
b) B \(=\)\(\left(2-\dfrac{a-3\sqrt{a}}{\sqrt{a}-3}\right)\)\(.\)\(\left(2-\dfrac{5\sqrt{a}-\sqrt{ab}}{\sqrt{b}-5}\right)\)
c) C = \(\left(\dfrac{x-\sqrt{x}}{\sqrt{x}-1}+2\right)\)\(.\)\(\left(2-\dfrac{\sqrt{x}+x}{1+\sqrt{x}}\right)\)
GIÚP MÌNH VS MAI MÌNH NỘP BÀI RỒI
Giải phương trình:
a) \(\sqrt{x+3}+\sqrt{6-x}-\sqrt{\left(x+3\right)\left(6-x\right)}=3\)
b) \(\sqrt{x-1}+\sqrt{x+3}+2\sqrt{\left(x-1\right)\left(x+3\right)}=4-2x\)
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,\(E=\dfrac{15\sqrt{x}-11}{x+2\sqrt{x}-3}+\dfrac{3\sqrt{x}-2}{1-\sqrt{x}}-\dfrac{2\sqrt{x}+3}{\sqrt{x}+3}\)
Bài 1: Tìm GTNN A=\(\left(3\sqrt{x}-2\right)^2-\left(\sqrt{x}+2\right)^2\) B=\(\left(\sqrt{x}+6\right)^2+\left(\sqrt{x}-2\right)^2+7\) Bài 2: Tìm GTLN A=\(\left(\sqrt{x}-3\right)^2+\left(2\sqrt{x}+3\right)^2\) B=\(2018-x-y+2\sqrt{x}+4\sqrt{x}\) (x,y>=0) C=\(\dfrac{5x^2+17}{2x^2+1}\) Giúp mk vs mk cần vào T7 mong mn giúp đỡ nhiều. Mk xin cảm ơn ạ.
