ĐKXĐ: ...
Đặt \(\sqrt{\frac{x+7}{3}}=a+1\)
\(\Rightarrow\frac{x+7}{3}=a^2+2a+1\)
\(\Rightarrow x+7=3a^2+6a+3\)
Ta được hệ:
\(\left\{{}\begin{matrix}3x^2+6x-3=a+1\\x+7=3a^2+6a+3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x^2+6x=a+4\\3a^2+6a=x+4\end{matrix}\right.\)
\(\Leftrightarrow...\)
Giải pt
a) \(2x^2+\sqrt{x^2-5x-6}=10x+15\)
b) \(5\sqrt{3x^2-4x-2}-6x^2+8x+7=0\)
c) \(x^2+\sqrt{2x^2+4x+3}=6-2x\)
d) \(2\sqrt{\frac{3x-1}{x}}=\frac{x}{3x-1}+1\)
e) \(\sqrt{\frac{24x-4}{x}}=\frac{x}{6x-1}+1\)
f) \(\sqrt{\frac{2x-1}{x}}+1+\sqrt{\frac{x}{2x-1}}=\frac{3x}{2x-1}\)
giải pt
a) \(\frac{3-2\sqrt{x^2+3x+2}}{1-2\sqrt{x^2-x+1}}=1\)
b) \(\sqrt{3x^2-5x+7}+\sqrt{3x^2-7x+2}=3\)
c) \(\sqrt{x^2+3x+2}+\sqrt{x^2+6x+5}=\sqrt{2x^2+9x+7}\)
d) \(\sqrt{x^2-1}-\sqrt{x^2+3}+\sqrt{5-x}=0\)
e) \(\left(x-1\right)\sqrt{1+x\sqrt{x^2+4}}=x^2-1\)
giải pt
a) \(3\sqrt{x}+\frac{3}{2\sqrt{x}}=2x+\frac{1}{2x}-7\)
b) \(5\sqrt{x}+\frac{5}{2\sqrt{x}}=2x+\frac{1}{2x}+4\)
c) \(\sqrt{2x^2+8x+5}+\sqrt{2x^2-4x+5}=6\sqrt{x}\)
d) \(x+1+\sqrt{x^2-4x+1}=3\sqrt{x}\)
e) \(x^2+2x\sqrt{x-\frac{1}{x}}=3x+1\)
f) \(x^2-6x+x\sqrt{\frac{x^2-6}{x}}-6=0\)
g) \(\frac{3x^2}{3+\sqrt{x}}+6+2\sqrt{x}=5x\)
h) \(\frac{x^2}{4-3\sqrt{x}}+8=3\left(x+2\sqrt{x}\right)\)
giải hệ phương trình:
\(\left\{{}\begin{matrix}6\sqrt{6x^3+x^2+x-5}=\left(x-\frac{4}{x}+7\right)\left(x^2+\frac{4}{x}\right)\\2\sqrt{3x}+x+5=\left(y+1\right)^2\end{matrix}\right.\)
Giải các phương trình sau:
a, \(\sqrt{4x-1}+4x^2-6x+1=0\)
b, \(\sqrt{3x^2-2x+9}+\sqrt{3x^2-2x+2}=7\)
c,\(3\sqrt{x}+8=9x+\frac{1}{x}+\frac{1}{\sqrt{x}}\)
d, \(\frac{2x^2+8x+1}{2x+1}=5\sqrt{x}\)
1. \(x^3-x^2+12x\sqrt{x-1}+20=0\)
2. \(x^3+\sqrt{\left(x-1\right)^3}=9x+8\)
3. \(\sqrt{2x^2+x+1}+\sqrt{x^2-x+1}=3x\)
4. \(x^6+\left(x^3-3\right)^3=3x^5-9x^2-1\)
5. \(x^2-6\left(x+3\right)\sqrt{x+1}+14x+3\sqrt{x+1}+13=0\)
6. \(x^2-4x+\left(x-3\right)\sqrt{x^2-x+1}=-1\)
7. \(\sqrt{2x-1}+\sqrt{5-x}=x-2+2\sqrt{-2x^2+11x-5}\)
8. \(\sqrt{5x+11}-\sqrt{6-x}+5x^2-14x-60=0\)
9. \(x^2+6x+8=3\sqrt{x+2}\)
10. \(2x^2+3x-2=\left(2x-1\right)\sqrt{2x^2+x-3}\)
11. \(\sqrt{x+1}+\sqrt{4-x}-\sqrt{\left(x+1\right)\left(4-x\right)}=1\)
12. \(x^2-\sqrt{x^2-4x}=4\left(x+3\right)\)
13. \(x^2-x-4=2\sqrt{x-1}\left(1-x\right)\)
14. \(\frac{1}{\sqrt{x}+1}+\frac{1}{\sqrt{x}-1}=1\)
15. \(\sqrt{2x^2+3x+2}+\sqrt{4x^2+6x+21}=11\)
16. \(\sqrt{x+3+3\sqrt{2x-3}}+\sqrt{x-1+\sqrt{2x-1}}=2\sqrt{2}\)
17. \(\left(x-2\right)^2\left(x-1\right)\left(x-3\right)=12\)
18. \(2x^2+\sqrt{x^2-2x-19}=4x+74\)
19. \(x^4+x^2-20=0\)
20. \(x+\sqrt{4-x^2}=2+3x\sqrt{4-x^2}\)
21. \(\left(x^2+x+1\right)\left(\sqrt[3]{\left(3x-2\right)^2}+\sqrt[3]{3x-2}+1\right)=9\)
22. \(\sqrt{x^2-3x+5}+x^2=3x+7\)
23. \(x^2+6x+5=\sqrt{x+7}\)
24. \(\frac{2x^2-3x+10}{x+2}=3\sqrt{\frac{x^2-2x+4}{x+2}}\)
25. \(5\sqrt{x-1}-\sqrt{x+7}=3x-4\)
26. \(2\left(x^2+2\right)=5\sqrt{x^3+1}\)
27. \(\sqrt{x-1}+\sqrt{5-x}-2=2\sqrt{\left(x-1\right)\left(5-x\right)}\)
28. \(x^2+\frac{9x^2}{\left(x-3\right)^2}=40\)
29. \(\frac{26x+5}{\sqrt{x^2+30}}+2\sqrt{26x+5}=3\sqrt{x^2+30}\)
30. \(\frac{\sqrt{27+x^2+x}}{2+\sqrt{5-\left(x^2+x\right)}}=\frac{\sqrt{27+2x}}{2+\sqrt{5-2x}}\)
Giải các phương trình sau:
a)\(\frac{2x-5}{2x^2+3x-5}+\frac{3x+1}{1-x}=\frac{x+20}{4x+10}\)
b)\(\sqrt{5x+1}=\sqrt{14x+7}+\sqrt{2x+3}\)
c)\(\sqrt{x+3}-\sqrt{x+1}=\sqrt{5x+7}\)
d)\(\sqrt{\left(x-3\right)^2\left(x-1\right)}=x-3\)
e)\(\sqrt{x^2+2x+2}=1-x\)
f)\(\sqrt{x^4+x^2+4}=x^2+2\)
g)\(2x^2-6x+1=\sqrt{4x+5}\)
h)\(x^2+\sqrt{x+11}=11\)
giải pt
a) \(\sqrt{x+3}=3-\sqrt{6-x}\)
b) \(\sqrt{3x-2}-\sqrt{x-7}=1\)
c) \(\frac{1-\sqrt{3x+1}}{\sqrt{x-1}-7}=1\)
d) \(\frac{x}{\sqrt{7x-4}-3}=\frac{x}{\sqrt{x+1}}\)
e) \(\sqrt{3x-2}-\sqrt{x-7}=1\)
f) \(2\sqrt{\frac{3x+1}{2x-1}}-\sqrt{\frac{x-1}{2x-1}}=2\)
giai pt:
a) \(\frac{3x+\sqrt{x^2-x-1}}{x+1}=\frac{7}{3}\)
b) \(\frac{2}{2\sqrt{x^2-2x+1}}=\frac{1}{x-1}\)
c) \(\frac{6}{6-\sqrt{x}}+\frac{1}{\sqrt{x}}=1\)
d) \(\frac{2}{\sqrt{x-1}}+\sqrt{x-1}=\frac{3\sqrt{x-1}+1}{\sqrt{x-1}}-1\)
e) \(\sqrt{x+3-\sqrt{x-1}=2}\)
f) \(\sqrt{x^3+x^2+6x+28}=x+5\)
g) \(\sqrt{x^4-4x^3+14x-11}=1-x\)
Giải hệ phương trình:
\(\left\{{}\begin{matrix}y^3-4y^2+4y=\sqrt{x+1}\left(y^2-5y+4+\sqrt{x+1}\right)\\2\sqrt{x^2-3x+3}+6x-7=y^2\left(x-1\right)^2+\left(y^2-1\right)\sqrt{3x-2}\end{matrix}\right.\)
