\(\sqrt{x+3}=2\)
\(\Leftrightarrow\)\(x+3=4\)
\(\Leftrightarrow\)\(x+3=4\) hoặc\(x+3=-4\)
\(\Leftrightarrow\)x=1;-7
Vậy x={1;-7}
\(\sqrt{x+3}=2\)
nên x+3=4
hay x=1
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 = \(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
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
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)\(\dfrac{x^2-5}{x+\sqrt{5}}\left(x\ne-\sqrt{5}\right)\)
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. \(\dfrac{3\sqrt{x-5}}{\sqrt{x+1}}\ge0\)
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) \(\sqrt{6x-3}+2=\sqrt{3}\)
\(\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}\right)\)
\(\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}}{\sqrt{x}+3}\right)\)
Câu1: Rút gọn
\(a,x+\sqrt{\left(x+2\right)^2}\cdot\left(x-2\right)\\ b,\sqrt{m^2-6m+9-2m}\left(x>3\right)\\ c,1+\sqrt{\frac{\left(x-1\right)^2}{x-1}}\\ d,\sqrt{x+4\sqrt{x-4}}+\sqrt{x-4\sqrt{x-4}}\)
Câu 2: So sánh
\(a,3và\sqrt{5}\\ \\ \\ b,2\sqrt{2}và3\sqrt{2}\\ \\ \\ c,-4\sqrt{5}và-6\sqrt{6}\\ \\ \\ d,2\sqrt{3}-5và\sqrt{3}-4\\ \\ \\e,A=\sqrt{2006}-\sqrt{2005}và\\ B=\sqrt{2005}-\sqrt{2004}\)
Câu 3: Rút gọn
\(a,\sqrt{16-2\sqrt{55}}\\ \\ \\ \\ \\ \\ \\ \\ \\ b,\sqrt{14-6\sqrt{5}}\\ \\ \\ \\ \\ \\ \\ \\ \\ c,\sqrt{36+12\sqrt{5}}\\ \\ \\ \\ \\ \\ \\ \\ \\ d,\sqrt{29+12\sqrt{5}}\)
Câu4: Tìm đkxđ
\(a,\sqrt{x^2-9}\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ b,\sqrt{x^2-3x+2}\)
\(c,\frac{\sqrt{x+3}}{\sqrt{5-x}}\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ d,\sqrt{\frac{x+3}{5-x}}\)
Giúp mình nhé!!
2. Rut gon bieu thuc:
a) \(A=\sqrt{x-2+2\sqrt{x-3}}+\sqrt{x+6+6\sqrt{x-3}},voix>=3\)
3. Tim GTNN cua bieu thuc:
a) \(A=\sqrt{4x^2-12x+9}+\sqrt{x^2-10x+25}+\sqrt{9x^2-6x+1}+\sqrt{16x^2-72x+81}\)
b) \(B=\dfrac{1}{2}\sqrt{x^2}+\sqrt{x^2-2x+1}\)
Tìm x để mỗi căn thức sau có nghĩa:
a. \(\sqrt{3-2x}\) b. \(\sqrt{x+1}+\sqrt{3-x}\) c. \(\dfrac{\sqrt{4x-2}}{x^2-4x+3}\) d. \(\dfrac{\sqrt{4x^2-2x+1}}{\sqrt{3-5x}}\)
