\(\sqrt{x-6-4\sqrt{x-2}}=5\)
\(\sqrt{x-6-\sqrt{\left(2x-2\right)^2}}=5\)
\(\sqrt{x-6-2x-2}=5\)
\(\sqrt{-x-8}=5\)
\(\left\{{}\begin{matrix}5\ge0\left(luon\cdot dung\right)\\-x-8=25\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}5\ge0\left(luon\cdot dung\right)\\x=-33\left(l\right)\end{matrix}\right.\)
Giải các phương trình vô tỉ (Phương trình có chứa căn thức)
1) \(\sqrt{x^2-20x+100}=10\)
2) \(\sqrt{x+2\sqrt{x}+1}=6\)
3) \(\sqrt{x^2-6x+9}=\sqrt{4+2\sqrt{3}}\)
4) \(\sqrt{3x+2\sqrt{3x}+1}=5\)
5) \(\sqrt{x^2+2x\sqrt{3}+3}=\sqrt{4-2\sqrt{3}}\)
6) \(\sqrt{6x+4\sqrt{6x}+4}=7\)
7) \(\sqrt{2x^2-2x\sqrt{6}+3}-\sqrt{5-\sqrt{24}}=0\)
8) \(\sqrt{3-2\sqrt{2}}-\sqrt{x^2-2x\sqrt{2}+2}=0\)
9) \(\sqrt{11-\sqrt{120}}=\sqrt{5x^2+x\sqrt{120}+6}\)
Giải phương trình :
a,\(\sqrt{x-2-2\sqrt{x-3}}-\sqrt{x+1-4\sqrt{x-3}}=2\)
b,\(\sqrt{2x-1+2\sqrt{x^2-x}}+\sqrt{2x-1-2\sqrt{x^2-x}}=5\) với \(x\frac{>}{ }1\)
c,\(\sqrt{x+6-4\sqrt{x+2}}+\sqrt{x+11-6\sqrt{x+2}}=1\)
1. Tính:
a) \(\sqrt{243}-\frac{1}{2}\sqrt{12}-2\sqrt{75}+\sqrt{27}\)
b) \(\frac{2\sqrt{3}-3\sqrt{2}}{\sqrt{3}-\sqrt{2}}+\frac{5}{1+\sqrt{6}}-6\sqrt{\frac{1}{6}}\)
2. Rút gọn: \(\frac{\sqrt{x}+1}{\sqrt{x}-2}+\frac{2\sqrt{x}}{\sqrt{x}+2}+\frac{2+5\sqrt{x}}{4-x}\)
Giải phương trình \(\sqrt{8x+1}+\sqrt{3x-5}=\sqrt{7x+4}+\sqrt{2x-2}\)
\(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1\)
\(\sqrt{6-x}+\sqrt{x+2}=x^2-6x+13\)
\(\sqrt{x^2-x}+\sqrt{x^2+x-2}=0\)
a. \(x+\sqrt{x}-2\)
b. \(x-9\)
c. \(x-3\sqrt{x}+2\)
d. \(x-5\sqrt{x}-6\)
e. \(x-4\)
f. \(x+7\sqrt{x}+12\)
g. \(x+\sqrt{x}\)
\(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8+6\sqrt{x-1}}=5\)
\(x^{2^{ }}+\sqrt{x+5}=5\)
Giải phương trình:
*\(\sqrt{x^2-4x+5}+\sqrt{x^2-4x+8}+\sqrt{x^2-4x+9}=3+\sqrt{5}\)
*\(\sqrt{x+3-4\sqrt{x-1}+\sqrt{x+8+6\sqrt{x-1}=5}}\)
giải các pt
1, \(\sqrt{2x^2+8x+6}+\sqrt{x^2-1}=2x+2\)
2, \(\sqrt{x+2\sqrt{x-1}}-\sqrt{x-2\sqrt{x-1}}=2\)
3, \(\sqrt{x^2+x+4}+\sqrt{x^2+x+1}=\sqrt{2x^2+2x+9}\)
4, \(2x^2+\sqrt{x^2-4x+12}=4x+8\)
5, \(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1\)
Giải phương trình
a,\(\sqrt{x-2+-\sqrt{2x-5}}+\sqrt{x+2+3\sqrt{2x+5}}=7\sqrt{2}\)
b,\(\sqrt{x+2-4\sqrt{x-2}}+\sqrt{x+7-6\sqrt{x}-2}=1\)
Giải phương trình:
a) \(\sqrt{x^2-4x+4}+\left|x-4\right|=0\)
b) \(\sqrt{x^2-1}+1=x^2\)
c) \(\sqrt{x+5}=1-x\)
d) \(\sqrt{x^2-2x+1}=\sqrt{6+4\sqrt{2}}-\sqrt{6-4\sqrt{2}}\)
