Giải hệ pt

1/\(\left\{{}\begin{matrix}4x\sqrt{y+1}+8x=\left(4x^2-4x-3\right)\sqrt{x+1}\\\dfrac{x}{x+1}+x^2=\left(y+2\right)\sqrt{\left(x+1\right)\left(y+1\right)}\end{matrix}\right.\)

2/\(\left\{{}\begin{matrix}x\sqrt{y^2+6}+y\sqrt{x^2+3}=7xy\\x\sqrt{x^2+3}+y\sqrt{y^2+6}=x^2+y^2+2\end{matrix}\right.\)\(\left\{{}\begin{matrix}x\sqrt{y^2+6}+y\sqrt{x^2+3}=7xy\\x\sqrt{x^2+3}+y\sqrt{y^2+6}=x^2+y^2+2\end{matrix}\right.\)

3/\(\left\{{}\begin{matrix}\left(2x+y-1\right)\left(\sqrt{x+3}+\sqrt{xy}+\sqrt{x}\right)=8\sqrt{x}\\\left(\sqrt{x+3}+\sqrt{xy}\right)^2+xy=2x\left(6-x\right)\end{matrix}\right.\)\(\left\{{}\begin{matrix}\left(2x+y-1\right)\left(\sqrt{x+3}+\sqrt{xy}+\sqrt{x}\right)=8\sqrt{x}\\\left(\sqrt{x+3}+\sqrt{xy}\right)^2+xy=2x\left(6-x\right)\end{matrix}\right.\)

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

m.n giúp e mấy bài này vs ạ!!

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

a)\(3\sqrt{40\sqrt{12}}+4\sqrt{\sqrt{75}}-5\)\(\sqrt{5\sqrt{48}}\)

b)\(\sqrt{8\sqrt{3}}+3\sqrt{20\sqrt{3}}-2\sqrt{45\sqrt{3}}\)

c)\(\left(\sqrt{x}-1\right).\left(x+\sqrt{x}+1\right)\left(x\ge0;y\ge0\right)\)

d)\(\left(\sqrt{x}+1\right)\left(x+1-\sqrt{x}\right)\left(x\ge0;y\ge0\right)\)

e)\(\left(\sqrt{x}+y\right)\left(x+y^2-y\sqrt{2}\right)\left(x\ge0;y\ge0\right)\)

giải hệ: a, \(\left\{{}\begin{matrix}x^2+\frac{1}{y^2}+\frac{x}{y}=3\\x+\frac{1}{y}+\frac{x}{y}=3\end{matrix}\right.\)

b, \(\left\{{}\begin{matrix}\sqrt[]{x-1}+\sqrt[]{y-1}=2\\\frac{1}{x}+\frac{1}{y}=1\end{matrix}\right.\)

c,\(\left\{{}\begin{matrix}x\sqrt[]{x}+y\sqrt[]{y}=35\\x\sqrt[]{y}+y\sqrt[]{x}=30\end{matrix}\right.\)

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

e,\(\left\{{}\begin{matrix}\left(\frac{x}{y}\right)^3+\left(\frac{x}{y}\right)^2=12\\\left(xy\right)^2+xy=6\end{matrix}\right.\)

Giải giúp mình nha

1/ Thực hiện phép tính

a) \(\sqrt{9-2\sqrt{20}}+\sqrt{12-2\sqrt{35}}\)

b) \(\sqrt{5-\sqrt{21}}-\sqrt{5+\sqrt{21}}\)

2/Rút gọn biểu thức

a) \(\sqrt{\frac{\left(x-2\right)^4}{\left(3-x\right)^2}}+\frac{x^2-1}{x-3}\left(x< 3\right)\)

b) \(4x-\sqrt{8}+\frac{\sqrt{x^3+2x^2}}{\sqrt{x+2}}\left(x>-2\right)\)

3/ Phân tích thành nhân tử

a) \(\sqrt{x}+\sqrt{y}-5\sqrt{xy}-5y\left(x,y\ge0\right)\)

b) \(x\sqrt{x}-y\sqrt{y}\left(x,y\ge0\right)\)

Giải hệ ạ

câu a

• \(x\left(x+y+1\right)-3=0\)
• \(\left(x+y\right)^2-\frac{5}{x^2}+1=0\)​

Câu b

• \(x^2+y^2=2\)
• \(\left(x+y\right)\left(1+xy\right)^4=32\)​

Câu c

• \(\left(12.x-7\right)\sqrt{3.x-2}+y\left(4y^2+1\right)=0\)
• \(\sqrt{x-1}+\sqrt{3-x}=\left(x-1\right)\left(y^2-2\right)\)

Câu d

• \(8.x^3+2.x+\left(2.y-6\right)\sqrt{5-2y}=0\)
• \(4.x^2+y^2-2\sqrt{3-4.x^2}=4\)

Câu e

• \(1+x^3y^3=19.x^3\)
• \(y+xy^2=-6.x^2\)

Câu f

• \(x\left(x+y+1\right)-3=0\)
• \(\left(x+y\right)^2-\frac{5}{x^2}+1=0\)​​​

Ai giải giùm em mấy câu này em cảm ơn nhiều ạ

Rút gọn

a)\(3\sqrt{40\sqrt{12}}+4\sqrt{\sqrt{75}}-5\)\(\sqrt{5\sqrt{48}}\)

b)\(\sqrt{8\sqrt{3}}+3\sqrt{20\sqrt{3}}-2\sqrt{45\sqrt{3}}\)

c)\(\left(\sqrt{x}-1\right).\left(x+\sqrt{x}+1\right)\left(x\ge0;y\ge0\right)\)

d)\(\left(\sqrt{x}+1\right)\left(x+1-\sqrt{x}\right)\left(x\ge0;y\ge0\right)\)

e)\(\left(\sqrt{x}+y\right).\left(x+y^2-y\sqrt{2}\right)\left(x\ge0;y\ge0\right)\)

chứng minh

a. \(\frac{x\sqrt{x}+y\sqrt{y}}{\sqrt{x}+\sqrt{y}}-\left(\sqrt{x}-\sqrt{y}\right)^2=\sqrt{xy}\)

b. \(\frac{\sqrt{x+2\sqrt{x-2}-1}.\left(\sqrt{x-2}-1\right)}{\sqrt{x}-3}=\sqrt{x}+\sqrt{3}\) Với x \(\ge\)2; x \(\ne\)3

c.\(\left(\frac{1}{a-\sqrt{a}}+\frac{1}{\sqrt{a}-1}\right):\frac{\sqrt{a}+1}{a-2\sqrt{a}+1}=\frac{\sqrt{a}-1}{\sqrt{a}}\) Với a > 0; a \(\ne\)1

d.\(\sqrt{\frac{x-6\sqrt{x}+9}{x+6\sqrt{x}+9}}\) Với x \(\ge\) 0

e. \(\left(x-y\right).\sqrt{\frac{xy}{\left(x-y\right)^2}}\)