ĐK: \(x\ge-4\)
\(\sqrt{6-4x+x^2}-x=4\Leftrightarrow\sqrt{6-4x+x^2}=4+x\Leftrightarrow6-4x+x^2=\left(4+x\right)^2\Leftrightarrow6-4x+x^2=16+8x+x^2\Leftrightarrow12x=-10\Leftrightarrow x=\frac{-5}{6}\left(tm\right)\)Vậy S={\(-\frac{5}{6}\)}
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 các phương trình:
1) \(\sqrt{x^2-2x+1}=x^2-1\)
2) \(\sqrt{4x^2-4x+1}=x-1\)
3) \(\sqrt{x^4-2x^2+1}=x-1\)
4) \(\sqrt{x^2+x+\frac{1}{4}}=x\)
5) \(\sqrt{x^4-8x^2+16}=2-x\)
6) \(\sqrt{9x^2+6x+1}=\sqrt{11-6\sqrt{2}}\)
Bài 2
a) A= \(\sqrt{\left(1-\sqrt{2}\right)^2}+\sqrt{\left(-2\right)^6}-\sqrt{\left(1+\sqrt{2}\right)^2}\)
b) B= \(\sqrt{7+2\sqrt{6}}+\sqrt{7-2\sqrt{6}}\)
c) C= \(\sqrt{7-4\sqrt{3}}\)
d) D= \(2\sqrt{7+4\sqrt{3}}-\sqrt{13-4\sqrt{3}}\)
e) E= \(\frac{1}{1+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+...+\frac{1}{\sqrt{79}+\sqrt{81}}\)
Bài 4:
a) \(\sqrt{x-1}=2\)
b) \(\sqrt{x^2-3x+2}=\sqrt{2}\)
c) \(\sqrt{4x+1}=x+1\)
d) \(\sqrt{x+2\sqrt{x-1}}-\sqrt{x-2\sqrt{x-1}}=2\)
e) \(\sqrt{x^2-4x+5}+\sqrt{x^2-4x+8}+\sqrt{x^2-4x+9}=3+\sqrt{5}\)
f)
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) \(\sqrt{x^2-2x+1}=\sqrt{6+4\sqrt{2}}-\sqrt{6-4\sqrt{2}}\)
\(\sqrt{7-\frac{1}{5}x}\) 2) \(\sqrt{\frac{4}{3}+2x}\)
\(\sqrt{\frac{2}{x^2+\frac{1}{2}}}\) 4) \(\sqrt{\frac{-2}{x^2+\frac{1}{3}}}\)
\(\sqrt{\frac{-5}{x^2+4x}}\) 6) \(\sqrt{\frac{5}{x^2+4x}}\)
\(\sqrt{\frac{2}{x^2+3x-4}}\) 8)\(\sqrt{\frac{2}{3x^2+5x-8}}\)
\(\sqrt{\frac{-6}{x^2-25}}\) 10)\(\sqrt{\frac{-7}{4x^2-9}}\)
\(\sqrt{\frac{2}{4x^2+x+3}}\) Gỉai phương trình
Giúp mk vs các bn mk bí rồi.
Giải phương trình:
a) \(\sqrt{4x^2-4x+1}=2x+1\)
b) \(\sqrt{x+3}+4\sqrt{x}-2x=6-\sqrt{5-x}\)
Sử dụng hằng đẳng thức \(\sqrt{A^2}\)= \(\)IAI để giải pt:
a) \(\sqrt{9-12x+4x^2}\)= 4 + x
b) \(\sqrt{4-4x+x^2}\)= ( x - 1 )2 + x - 6
Tìm x: \(a.\sqrt{4-5x}=12\)
\(b.\sqrt{10+\sqrt{3x}}=2+\sqrt{6}\)
c. \(\sqrt{4x+20}-3\sqrt{5+x}+\frac{4}{3}\sqrt{9x+45}=6\)
d. \(\sqrt{x^2-9}-3\sqrt{x-3}=0\)
e. \(\sqrt{\frac{4x+3}{x+1}}=3\)
f. \(\sqrt{x-2}\le3\)
