Giải hệ phương trình:

1. \(\left\{{}\begin{matrix}x+3=2\sqrt{\left(3y-x\right)\left(y+1\right)}\\\sqrt{3y-2}-\sqrt{\dfrac{x+5}{2}}=xy-2y-2\end{matrix}\right.\)

2. \(\left\{{}\begin{matrix}\sqrt{2y^2-7y+10-x\left(y+3\right)}+\sqrt{y+1}=x+1\\\sqrt{y+1}+\dfrac{3}{x+1}=x+2y\end{matrix}\right.\)

3. \(\left\{{}\begin{matrix}\sqrt{4x-y}-\sqrt{3y-4x}=1\\2\sqrt{3y-4x}+y\left(5x-y\right)=x\left(4x+y\right)-1\end{matrix}\right.\)

4. \(\left\{{}\begin{matrix}9\sqrt{\dfrac{41}{2}\left(x^2+\dfrac{1}{2x+y}\right)}=3+40x\\x^2+5xy+6y=4y^2+9x+9\end{matrix}\right.\)

5. \(\left\{{}\begin{matrix}\sqrt{xy+\left(x-y\right)\left(\sqrt{xy}-2\right)}+\sqrt{x}=y+\sqrt{y}\\\left(x+1\right)\left[y+\sqrt{xy}+x\left(1-x\right)\right]=4\end{matrix}\right.\)

6. \(\left\{{}\begin{matrix}x^4-x^3+3x^2-4y-1=0\\\sqrt{\dfrac{x^2+4y^2}{2}}+\sqrt{\dfrac{x^2+2xy+4y^2}{3}}=x+2y\end{matrix}\right.\)

7. \(\left\{{}\begin{matrix}x^3-12z^2+48z-64=0\\y^3-12x^2+48x-64=0\\z^3-12y^2+48y-64=0\end{matrix}\right.\)

Giải các hệ phương trình sau:

a) \(\left\{{}\begin{matrix}4x^2-4xy-14x-3y^2+y+10=0\\5\sqrt{xy}+2x+2y=6\sqrt{y}-8\end{matrix}\right.\)

b) \(\left\{{}\begin{matrix}2x^4+3x^2y+4x^2-2y^2+3y+2=0\\\sqrt{x\left(y-1\right)}+2y+2\sqrt{y-1}=3x+2\sqrt{x}+2\end{matrix}\right.\)

c) \(\left\{{}\begin{matrix}x^6+3x^2-y^3-6y^2-15y-14=0\\\sqrt{xy+2x-y-2}+6x-2y=10\end{matrix}\right.\)

d) \(\left\{{}\begin{matrix}xy+x+y=x^2-2y^2\\x\sqrt{2y}-y\sqrt{x-1}=2x-2y\end{matrix}\right.\)

a)Giải các phương trình sau bằng phương pháp đặt ẩn phụ:
1) \(x^2-3x-3=\frac{3\left(\sqrt[3]{x^3-4x^2+4}-1\right)}{1-x}\)      ;2)\(1+\frac{2}{3}\sqrt{x-x^2}=\sqrt{x}+\sqrt{1-x}\)
b) Giải các phương trình sau(không giới hạn phương pháp):
1)\(2\left(1-x\right)\sqrt{x^2+2x-1}=x^2-2x-1\) ;  2)\(\sqrt{2x+4}-2\sqrt{2-x}=\frac{12x-8}{\sqrt{9x^2+16}}\)
3)\(\frac{3x^2+3x-1}{3x+1}=\sqrt{x^2+2x-1}\) ; 4) \(\frac{2x^3+3x^2+11x-8}{3x^2+4x+1}=\sqrt{\frac{10x-8}{x+1}}\)
5)\(13x-17+4\sqrt{x+1}=6\sqrt{x-2}\left(1+2\sqrt{x+1}\right)\);
6)\(x^2+8x+2\left(x+1\right)\sqrt{x+6}=6\sqrt{x+1}\left(\sqrt{x+6}+1\right)+9\)
7)\(x^2+9x+2+4\left(x+1\right)\sqrt{x+4}=\frac{5}{2}\sqrt{x+1}\left(2+\sqrt{x+4}\right)\)
8)\(8x^2-26x-2+5\sqrt{2x^4+5x^3+2x^2+7}\)

giải phương trình :

1,        \(\sqrt{4-x^2}+2\sqrt[3]{x^4-4x^3+4x^2}=\left(x-1\right)^2+1-\left|x\right|\)

2,        \(2x^3+9x^2-6x\left(1+2\sqrt{6x-1}\right)+2\sqrt{6x-1}+8=0\)

3,         \(x^3-3x+1=\sqrt{8-3x^2}\)

4,         \(\left(4x^2+x-1\right)\sqrt{x^2+x+2}=\left(4x^2+3x+5\right)\sqrt{x^2-1}\)

5,          \(\sqrt[3]{3-x^3}=2x^3+x-3\)

6,          \(\sqrt[3]{x^2+3x+3}+\sqrt[3]{2x^2+3x+2}=6x^2+12x+8\)

7,          \(\frac{x^2+2x-8}{x^2-2x+3}=\left(x+1\right)\left(\sqrt{x+2}-2\right)\)

8,          \(\frac{4x-1}{\sqrt{4x-3}}+\frac{11-2x}{\sqrt{5-x}}=\frac{15}{2}\)

9,          \(x^2-4x+14+\sqrt{x+4}=2\sqrt{1+12x}+\sqrt{1+\sqrt{1+12x}}\)

1) Giải hệ phương trình

\(\left\{{}\begin{matrix}3x^2+xy-4x+2y=2\\x\left(x+1\right)+y\left(y+1\right)=4\end{matrix}\right.\)

2) Giải phương trình

\(\sqrt{x^2-5x+4}+2\sqrt{x+5}=2\sqrt{x-4}+\sqrt{x^2+4x-5}\)

3) Tính giá trị của biểu thức

\(A=2x^3+3x^2-4x+2\)

Với \(x=\sqrt{2+\sqrt{\dfrac{5+\sqrt{5}}{2}}}+\sqrt{2-\sqrt{\dfrac{5+\sqrt{5}}{2}}}-\sqrt{3-\sqrt{5}}-1\)

4) Cho x, y thỏa mãn:

\(\sqrt{x+2014}+\sqrt{2015-x}-\sqrt{2014-x}=\sqrt{y+2014}+\sqrt{2015-y}-\sqrt{2014-y}\)

Chứng minh \(x=y\)

Giải phương trình:

1, \(\sqrt{x^2+2x}+\sqrt{2x-1}=\sqrt{3x^2+4x+1}\)

2, \(x^3-3x^2+2\sqrt{\left(x+2\right)^3}-6x=0\)

3, \(2x^3-x^2-3x+1=\sqrt{x^5+x^4+1}\)

4, \(5\sqrt{x^4+8x}=4x^2+8\)

5, \(\left(x^2+4\right)\sqrt{2x+4}=3x^2+6x-4\)

6, \(\left(x^2-6x+11\right)\sqrt{x^2-x+1}=2\left(x^2-4x+7\right)\sqrt{x-2}\)

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 hệ phương trình:

1, \(\left\{{}\begin{matrix}\left(17-3x\right)\sqrt{5-x}+\left(3y-14\right)\sqrt{4-y}=0\\2\sqrt{2x+y+5}+3\sqrt{3x+2y+11}=x^2+6x+13\end{matrix}\right.\)

2, \(\left\{{}\begin{matrix}x\left(x+y\right)+\sqrt{x+y}=\sqrt{2y}\left(\sqrt{2y^3}+1\right)\\x^2y-5x^2+7\left(x+y\right)-4=6\sqrt[3]{xy-x+1}\end{matrix}\right.\)

3, \(\left\{{}\begin{matrix}\sqrt{x}+\sqrt[4]{32-x}-y^2+3=0\\\sqrt[4]{x}+\sqrt{32-x}+6y-24=0\end{matrix}\right.\)