Đặt \(\sqrt{x^2-x+3}=t>0\)
\(t^2-2t-3=0\Rightarrow\left[{}\begin{matrix}t=-1\left(l\right)\\t=3\end{matrix}\right.\)
\(\Rightarrow x^2-x+3=9\Rightarrow x^2-x-6=0\Rightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)
Chương 3: PHƯƠNG TRÌNH, HỆ PHƯƠNG TRÌNH
Các câu hỏi tương tự
a,\(\sqrt{5X^2+X+3}-2\sqrt{5x-1}+X^2-3X+3=0\)
b,\(^{X^2-X-4+3X\sqrt{5-3X^2}=0}\)
1 tháng 10 2019 lúc 22:41
giải pt
a) \(x\sqrt{x^2-4x+3}=x^2+x\)
b) \(x^2+x-12-\left(x-3\right)\sqrt{10-x^2}=0\)
c) \(\sqrt{6+x-x^2}=\frac{\left(2x+5\right)\sqrt{6+x-x^2}}{x+4}\)
d) \(\sqrt{\frac{12+x-x^2}{2x+9}}-\frac{\sqrt{12+x-x^2}}{x+3}=0\)
e) \(\sqrt{x^3}+\sqrt{x^3+x^2+2x}=3\sqrt{x}\)
Giải phương trình:1. x^4-6x^2-12x-802. dfrac{x}{2x^2+4x+1}+dfrac{x}{2x^2-4x+1}dfrac{3}{5}3. x^4-x^3-8x^2+9x-9+left(x^2-x+1right)sqrt{x+9}04. 2x^2.sqrt{-4x^4+4x^2+3}4x^4+15. x^2+4x+3sqrt{dfrac{x}{8}+dfrac{1}{2}}6. left{{}begin{matrix}4x^3+xy^23x-y4xy+y^22end{matrix}right.7. left{{}begin{matrix}sqrt{x^2-3y}left(2x+y+1right)+2x+y-505x^2+y^2+4xy-3y-50end{matrix}right.8. left{{}begin{matrix}sqrt{2x^2+2}+left(x^2+1right)^2+2y-100left(x^2+1right)^2+x^2yleft(y-4right)0end{matrix}right.
Đọc tiếp
Giải phương trình:
1. \(x^4-6x^2-12x-8=0\)
2. \(\dfrac{x}{2x^2+4x+1}+\dfrac{x}{2x^2-4x+1}=\dfrac{3}{5}\)
3. \(x^4-x^3-8x^2+9x-9+\left(x^2-x+1\right)\sqrt{x+9}=0\)
4. \(2x^2.\sqrt{-4x^4+4x^2+3}=4x^4+1\)
5. \(x^2+4x+3=\sqrt{\dfrac{x}{8}+\dfrac{1}{2}}\)
6. \(\left\{{}\begin{matrix}4x^3+xy^2=3x-y\\4xy+y^2=2\end{matrix}\right.\)
7. \(\left\{{}\begin{matrix}\sqrt{x^2-3y}\left(2x+y+1\right)+2x+y-5=0\\5x^2+y^2+4xy-3y-5=0\end{matrix}\right.\)
8. \(\left\{{}\begin{matrix}\sqrt{2x^2+2}+\left(x^2+1\right)^2+2y-10=0\\\left(x^2+1\right)^2+x^2y\left(y-4\right)=0\end{matrix}\right.\)
\(x^2-3x+\sqrt{x^2-3x+2}=10\)\(3\sqrt{x^2-5x+10}=5x-x^2\)\(\left(x+4\right)\left(x-4\right)+3\sqrt{x^2-x+3}+5=0\)\(\left(x-3\right)\left(x+2\right)-2\sqrt{x^2-x+4}+10=0\)
Xem chi tiết
Giải hệ phương trình sau trên tập số thực:
\(\left\{{}\begin{matrix}\sqrt{x^2-y^2}-6=2\sqrt{x-y}-3\sqrt{x+y}\\3\sqrt{x-2}-2\sqrt[3]{y}+x^2+5y-15=0\end{matrix}\right.\)
7 tháng 8 2021 lúc 8:56
a) \(2\left(x^2-2x\right)+\sqrt{x^2-2x-3}-9=0\)
b) \(3\sqrt{2+x}-6\sqrt{2-x}+4\sqrt{4-x^2}=10-3x\)
c) Cho phương trình: \(\sqrt{x}+\sqrt{9-x}=\sqrt{-x^2+9x+m}\)
+) Giải phương trình khi m=9
+) Tìm m để phương trình có nghiệm
\(\left\{{}\begin{matrix}x^3-y^3+3y^2-3x-2=0\\x^2+\sqrt{1-x^2}-3\sqrt{2y-y^2}-1=0\end{matrix}\right.\)
9 tháng 8 2021 lúc 16:32
1/ \(x-\sqrt{2x+3}=0\)
2/\(\left(x+1\right)\left(x+4\right)-3\sqrt{x^2+5x+2}=6\)
3/\(1+\dfrac{2}{3}\sqrt{x-x^2}=\sqrt{x}+\sqrt{1-x}\)
1. x^3-x^2+12xsqrt{x-1}+200
2. x^3+sqrt{left(x-1right)^3}9x+8
3. sqrt{2x^2+x+1}+sqrt{x^2-x+1}3x
4. x^6+left(x^3-3right)^33x^5-9x^2-1
5. x^2-6left(x+3right)sqrt{x+1}+14x+3sqrt{x+1}+130
6. x^2-4x+left(x-3right)sqrt{x^2-x+1}-1
7. sqrt{2x-1}+sqrt{5-x}x-2+2sqrt{-2x^2+11x-5}
8. sqrt{5x+11}-sqrt{6-x}+5x^2-14x-600
9. x^2+6x+83sqrt{x+2}
10. 2x^2+3x-2left(2x-1right)sqrt{2x^2+x-3}
11. sqrt{x+1}+sqrt{4-x}-sqrt{left(x+1right)left(4-xright)}1
12. x^2-sqrt{x^2-4x}4left(...
Đọc tiếp
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. \(\frac{\sqrt{27+x^2+x}}{2+\sqrt{5-\left(x^2+x\right)}}=\frac{\sqrt{27+2x}}{2+\sqrt{5-2x}}\)
\(a,2x^2-9x+3+\sqrt{3x^2-7x+1}=0\)
b)\(\sqrt{x+2}+\sqrt{3-x}=x^3+x^2-4x-1\)
c)\(\text{4x^3-9x^2+7x-(3x-1)\sqrt{3x-2}=0}\)
d)\(2\sqrt{x-1}+\sqrt{5x-1}=x^2+1\)
e)\(\sqrt{x+2}+\sqrt{5x+6}+2\sqrt{8x+9}=4x^2\)
f)\(3x^2-x+3=\sqrt{3x+1}+\sqrt{5x+4}\)