\(\sqrt{x^2-2}-x+9=0\left(ĐKXĐ:x\ge\sqrt{2}hoặcx\le-\sqrt{2}\right)\)
\(\Leftrightarrow\sqrt{x^2-2}=x-9\left(ĐK:x\ge9\right)\\ \Leftrightarrow x^2-2=\left(x-9\right)^2=x^2-18x+81\\ \Leftrightarrow18x=83\\ \Leftrightarrow x=\dfrac{83}{18}\)
(không thỏa mãn ĐKXĐ)
Vậy phương trình vô nghiệm.
Giải các pt sau:
a)\(\left|3x+1\right|=\left|x+1\right|\)
b)\(\left|x^2-3\right|=\left|x-\sqrt{3}\right|\)
c)\(\sqrt{9x^2-12x+4}=\sqrt{x^2}\)
d)\(\sqrt{x^2+4x+4}=\sqrt{4x^2-12x+9}\)
e) \(\left|x^2-1\right|+\left|x+1\right|=0\)
f)\(\sqrt{x^2-8x+16}+\left|x+2\right|=0\)
g) \(\sqrt{1-x^2}+\sqrt{x+1}=0\)
h) \(\sqrt{x^2-4}+\sqrt{x^2+4x+4}=0\)
Mọi người giúp em gấp với!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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)\(\dfrac{x^2-5}{x+\sqrt{5}}\left(x\ne-\sqrt{5}\right)\)
Tìm x biết:
a, \(\sqrt{16x}\) = 8
b, \(\sqrt{x^2}\) = 2x -1
c, \(\sqrt{9\left(x-1\right)}\) = 21
d, \(\sqrt{4\left(1-x\right)^2}\) - 6 = 0
e, \(\sqrt{4\left(x^2-1\right)}\) - \(2\sqrt{15}\) = 0
f, \(\sqrt{x^2-25}-\sqrt{x-5}=0\)
g, \(\sqrt{9\left(2-3x\right)^2}=6\)
h, \(\sqrt{x+5}+\sqrt{5-x}=4\)
Giúp mình nhé!!
Bài 1: CMR:
a) \(\sqrt{\left(x-2\right)^2}+x+2=\left\{2\: x\left(voix>=2\right),4\left(voix< 2\right)\right\}\)
b)\(x-3+\sqrt{x^2-6x+9=}\left\{2\left(x-3\right)\left(voix>=3\right),0\left(voix< 3\right)\right\}\)
2.4 Rút gọn biểu thức
\(a,\dfrac{3-\sqrt{x}}{x-9}\) ( vs x ≥ 0, x≠ 9)
b, \(\dfrac{x-5\sqrt{x}+6}{\sqrt{x}-3}\)( vs x ≥ 0 ; x ≠ 9)
c, \(6-2x-\sqrt{9-6x+x^2}\left(x< 3\right)\)
a:\(\dfrac{b}{\left(a-4\right)^2}.\sqrt{\dfrac{\left(a-4\right)^4}{b^2}}\left(b>0;a\ne4\right)\)
b:\(\dfrac{x\sqrt{x}-y\sqrt{y}}{\sqrt{x}-\sqrt{y}}\left(x\ge0;y\ge0;x\ne0\right)\)
c:\(\dfrac{a}{\left(b-2\right)^2}.\sqrt{\dfrac{\left(b-2\right)^4}{a^2}\left(a>0;b\ne2\right)}\)
d:\(\dfrac{x}{\left(y-3\right)^2}.\sqrt{\dfrac{\left(y-3\right)^2}{x^2}\left(x>0;y\ne3\right)}\)
e:2x +\(\dfrac{\sqrt{1-6x+9x^2}}{3x-1}\)
Rút gọn biểu thức :
a) A = 4\(\sqrt{x}\)- \(\frac{\left(x+6\sqrt{x}+9\right)\left(\sqrt{x}-3\right)}{x-9}\)với 0 ≤ x ≠ 9 ;
b) B = \(\frac{\sqrt{9x^2+12x+4}}{3x+2}\)với x ≠ \(-\frac{2}{3}\)
Giải phương trình :
a) 13-\(\sqrt{\left(8x-1\right)^2}\) =\(\sqrt{x^2}\)
b) \(\sqrt{\left(x+1^2\right)}\)+\(\sqrt{\left(2x+3\right)^2}\)=3
c) \(\sqrt{\left(-x+\dfrac{2}{3}\right)^2}\)+ \(\sqrt{\left(x-1\dfrac{2}{5}\right)^2}\)+3=0
d) 6-\(\sqrt{x^2-6x+9}\)=\(\dfrac{5}{9}\)
Giúp mình với , mình đang cần gấp !!
\(\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}\right)\)
