a/
\(\Leftrightarrow\left\{{}\begin{matrix}x-2\ge0\\3x^2-9x+1=\left(x-2\right)^2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge2\\2x^2-5x-3=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge2\\\left[{}\begin{matrix}x=3\\x=-\frac{1}{2}\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow x=3\)
b/ ĐKXĐ: \(x\le2\)
\(\Leftrightarrow x^2-2x+4=2-x\)
\(\Leftrightarrow x^2-x+2=0\) (vô nghiệm)
Vậy pt vô nghiệm
giải phương trình sau \(2x^3-2x+\sqrt{2x^3-3x+1}=3x+1+\sqrt[3]{x^2+2}\)
Giải phương trình:
1, \(3x^2+6x-3=\sqrt{\dfrac{x+7}{3}}\) (2 cách khác nhau )
2, \(\left(\sqrt{3x+1}-\sqrt{x-2}\right)\left(\sqrt{3x^2+7x+2}+4\right)=4x-2\)
3, \(\sqrt{-3x-1}+\sqrt{9x^2+9x+3}=-9x^2-6x\)
4, \(\sqrt{x^2+x-6}+3\sqrt{x-1}=\sqrt{5x^2-1}\)
5, \(\left(\sqrt{x+4}+2\right)\left(x+2\sqrt{x-5}+1\right)=6x\)
6, \(\sqrt{5-x^4}-\sqrt[3]{3x^2-2}=1\)
7, \(3x^2+11+\sqrt{x-2}+\sqrt{2x+3}=14x\)
8, \(\sqrt{x-\sqrt{x-\sqrt{x-\sqrt{x-7}}}}=7\)
9, \(\sqrt{2x^2-1}+3x\sqrt{x^2-1}=3x^3+2x^2-9x-7\) ( với \(x>0\) )
Giải PT a, \(5\sqrt{2x^2+3x+9}=2x^2+3x+3\)
b. \(9-\sqrt{81-7x^3}=\frac{x^3}{2}\)
c. \(x^2+3-\sqrt{2x^2-3x+2}=\frac{3}{2}\left(x+1\right)\)
d. \(\sqrt{9x-2x^2}-9x+2x^2+6=0\)
e. \(\sqrt{x^2+x-1}+\sqrt{x-x^2+1}=x^2-x+2\)
f. \(\sqrt{x^2+x-5}+\sqrt{x-x^2+3}=x^2-3x+4\)
Giải các pt sau:
a) \(\sqrt{x+8}+\frac{9x}{\sqrt{x+8}}-6\sqrt{x}=0\)
b) \(x^4-2x^3+\sqrt{2x^3+x^2+2}-2=0\)
c) \(3x\sqrt[3]{x+7}\left(x+\sqrt[3]{x+7}\right)=7x^3+12x^2+5x-6\)
d) \(4x^2+\left(8x-4\right)\sqrt{x}-1=3x+2\sqrt{2x^2+5x-3}\)
e) \(16x^2+19x+7+4\sqrt{-3x^2+5x+2}=\left(8x+2\right)\left(\sqrt{2-x}+2\sqrt{3x+1}\right)\)
f) \(\left(5x+8\right)\sqrt{2x-1}+7x\sqrt{x+3}=9x+8-\left(x+26\right)\sqrt{x-1}\)
g) \(\sqrt[3]{3x+1}+\sqrt[3]{5-x}+\sqrt[3]{2x-9}-\sqrt[3]{4x-3}=0\)
Giải phương trình:
1. \(\sqrt{2x^2+4x+7}=x^4+4x^3+3x^2-2x-7\)
2. \(\dfrac{4}{x}+\sqrt{x-\dfrac{1}{x}}=x+\sqrt{2x-\dfrac{5}{x}}\)
3. \(\dfrac{6-2x}{\sqrt{5-x}}+\dfrac{6+2x}{\sqrt{5+x}}=\dfrac{8}{3}\)
4. \(x^2+1-\left(x+1\right)\sqrt{x^2-2x+3}=0\)
5. \(2\sqrt{2x+4}+4\sqrt{2-x}=\sqrt{9x^2+16}\)
6. \(\left(2x+7\right)\sqrt{2x+7}=x^2+9x+7\)
Giải phương trình 1, \(x^2+9x+7=\left(2x+1\right)\sqrt{2x^2+4x+5}\)
2, GPT \(\left(2x+7\right)\sqrt{2x+7}=x^2+9x+7\)
3. GHPT \(\left\{{}\begin{matrix}x^2-2y-1=2\sqrt{5y+8}+\sqrt{7x-1}\\\left(x-y\right)\left(x^2+xy+y^2+3\right)=3\left(x^2+y^2\right)+2\end{matrix}\right.\)
Giải phương trình:
1. \(x^2+3x+8=\left(x+5\right)\sqrt{x^2+x+2}\)
2. \(10x^2-9x-8x\sqrt{2x^2-3x+1}+3=0\)
3. \(x^3+6x^2-2x+3-\left(5x-1\right)\sqrt{x^3+3}=0\)
4. \(4\sqrt{x+1}-1=3x+2\sqrt{1-x}+\sqrt{1-x^2}\)
5. \(4\sqrt{x+3}=1+4x+\dfrac{2}{x}\)
Giải phương trình vô tỉ:
a) \(4x^2-4x-10=\sqrt{8x^2-6x-10}\)
b) \(\sqrt{\left(x+1\right)\left(2-x\right)}=1+2x-2x^2\)
c) \(\sqrt{3x+8+6\sqrt{3x-1}}+\sqrt{3x+8-6\sqrt{3x-1}}=3x+4\)
d) \(2x\sqrt{x^2-x+1}+4\sqrt{3x+1}=2x^2+2x+6\)
giải các phương trình sau :
a ) \(\sqrt{2x^2+16x+18}+\sqrt{x^2-1}=2x+4\)
b ) \(\sqrt{x^2+12}+5=3x+\sqrt{x^2+5}\)
