Đặt \(\sqrt{x^2+x+1}=a>0\)
Ta được \(a^2-2a=0\) \(\Leftrightarrow a\left(a-2\right)=0\)
Mà a > 0 => \(a-2=0\) \(\Leftrightarrow a=2\)
hay \(x^2+x+1=2\) \(\Leftrightarrow x^2+x-1=0\)
Gpt ta đc \(x_1=\dfrac{-1-\sqrt{5}}{2};x_2=\dfrac{-1+\sqrt{5}}{2}\)
A= x-2 2+ sqrt x (x>=0); ==( 8x sqrt x -1 2x- sqrt x - 8x sqrt x +1 2x+ sqrt x )= 2x+1 2x-1 vdi x>0,x ne 1 2 ;x ne- 1 2 MS05. Cho A =- a. Rút gọn B. b. Tim x d hat e A B =1
bài 1: rút gọn
A= \(\left(\dfrac{\sqrt{x}-1}{3\sqrt{x}1}-\dfrac{1}{3\sqrt{x}+1}+\dfrac{8\sqrt{x}}{9x-1}\right):\left(1-\dfrac{3\sqrt{x}-2}{3\sqrt{x}+1}\right)\) X>=0; x#0
B= \(\left(\dfrac{\sqrt{x}-2}{x-1}-\dfrac{\sqrt{x}+2}{x+2\sqrt{x}+1}\right):\left(\dfrac{2}{x^2-2x+1}\right)\) x>=0; x\(\ne\)1
bài 2:
\(\dfrac{1}{2x-3\sqrt{x}+2}\) x>=0
Tìm GTNN của A
,giải pt
a,\(\sqrt{x-2}-3\sqrt{x^2-4}=0\)
b,\(\sqrt{x^2-1}-x^2+1=0\)
Rút gọn biểu thức:
A=\(\left(\dfrac{2}{\sqrt{x}-1}-\dfrac{\sqrt{x}+1}{x-\sqrt{x}}\right).\left(\dfrac{x+\sqrt{x}}{\sqrt{x}+1}-\dfrac{2\sqrt{x}-2}{\sqrt{x}-1}\right)\)với x>0;x\(\ne\)1
\(\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\right).\left(\dfrac{1}{2\sqrt{x}}-\dfrac{\sqrt{x}}{2}\right)^2\)
rút gọn P
Tìm x để P =2
Tính P tại x = 3-\(2\sqrt{2}\)
Tìm x để P>0
1. giải phương trình chứa căn bậc 2
a) \(\sqrt{x^2-x+1}=x\)
b) \(\sqrt{x^2-3x+2}+\sqrt{x^2+x-6}=0\)
c) \(\sqrt{x^4-2x^2+1}=x-1\)
1.\(\sqrt{x^2+x}=x\)
2. \(\sqrt{1-x^2}=x-1\)
3.\(\sqrt{x^2-4x+3}=x-2\)
4. \(\sqrt{x^2-1}-x^2+1=0\)
5. \(\sqrt{x^2-4}-x+2=0\)
6. \(\sqrt{1-2x^2}=x-1\)
Tìm x
a)\(2\sqrt{2}-\dfrac{1}{2}.\sqrt{x}=0\)
b)\(2.\sqrt{x}-\sqrt{\dfrac{x}{3}}=1\)
c)\(4.\sqrt{x}+\sqrt{\dfrac{x}{2}}=\dfrac{1}{3}\)
Bài 11:
A= \(\left(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}}{x+\sqrt{x}+1}+\dfrac{1}{1-\sqrt{x}}\right):\dfrac{\sqrt{x}-1}{2}\)
a) Rút gọn A
b) CMR: 0 < A < 2
Rút gọn
a) với x>0 , x\(\ne\)1
\(\dfrac{\left(\sqrt{x^2+4}-2\right)\left(\sqrt{x^2+4}+2\right)\left(x+\sqrt{x}+1\right)\sqrt{x-2\sqrt{x}+1}}{x\left(x\sqrt{x}-1\right)}\)
b) với a>0,a\(\ne\)4
\(\left(\dfrac{\sqrt{a}-2}{\sqrt{a}+2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-2}\right)\left(\sqrt{a}-\dfrac{4}{\sqrt{a}}\right)\)
c)\(\left(\dfrac{\sqrt{a}-1}{\sqrt{a}+1}+\dfrac{\sqrt{a}+1}{\sqrt{a}-1}\right)\left(1-\dfrac{1}{\sqrt{a}}\right)\) với a>0 ,a\(\ne\)1
d)\(\dfrac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\dfrac{x^2+\sqrt{x}}{x-\sqrt{x}+1}+x+1\) với x>1
