\(=\frac{\left(\sqrt{x}+1\right).\sqrt{x}\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}{\left(x-y\right)x.\left(\sqrt{x}-1\right)}=\frac{\left(\sqrt{x}+1\right).\sqrt{x}.\left(x-y\right)}{\left(x-y\right).x.\left(\sqrt{x}-1\right)}=\frac{\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-1\right)}\)
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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!!
\(\left(\dfrac{x-y}{\sqrt{x}-\sqrt{y}}+\dfrac{x\sqrt{y}-y\sqrt{y}}{y-x}\right):\left(\dfrac{\left(\sqrt{x}-\sqrt{y}\right)^2+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\right)\) rút gọn ạ........mong m.n giúp với!!!!!..cảm ơn ạ
\(\left\{{}\begin{matrix}\sqrt{xy+\left(x-y\right)\left(\sqrt{xy}-2\right)}+\sqrt{x}=y+\sqrt{y}\\\left(x+1\right)\left(y+\sqrt{xy}+x-x^2\right)=4\end{matrix}\right.\)
1.\(\left\{{}\begin{matrix}x\left(x-2\right)\left(2x-y\right)=6\\\left(x-3\right)^2+2y=10\end{matrix}\right.\)
2. \(\left\{{}\begin{matrix}\frac{1}{\sqrt{x}}+\sqrt{2-\frac{1}{y}}=2\\\frac{1}{\sqrt{y}}+\sqrt{2-\frac{1}{x}}=2\end{matrix}\right.\)
3. \(\left\{{}\begin{matrix}\left(x+1\right)\left(y+1\right)=8\\x\left(x+1\right)+y\left(y+1\right)+xy=17\end{matrix}\right.\)
giải hpt: a,\(\left\{{}\begin{matrix}x+y-\sqrt{xy}=3\\\sqrt{x+1}+\sqrt{y+1}=4\end{matrix}\right.\) b,\(\left\{{}\begin{matrix}x+y=5+\sqrt{\left(x-1\right)\left(y-1\right)}\\\sqrt{x-1}+\sqrt{y-1}=3\end{matrix}\right.\)
Rút gọn biểu thức :
\(B=\dfrac{\sqrt{1+\sqrt{1-x^2}}\left[\left(1+x\right)\sqrt{1+x}-\left(1-x\right)\sqrt{1-x}\right]}{x\left(2+\sqrt{1-x^2}\right)}\)
Giúp mình với các cao nhân
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. \(\left\{{}\begin{matrix}x^3-12z^2+48z-64=0\\y^3-12x^2+48x-64=0\\z^3-12y^2+48y-64=0\end{matrix}\right.\)
tìm x,y,z để biểu thức sau có giá trị bằng 2
\(A=\dfrac{x}{\left(\sqrt{x}+\sqrt{y}\right)\left(1-\sqrt{y}\right)}-\dfrac{y}{\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}+1\right)}-\dfrac{xy}{\left(1+\sqrt{x}\right)\left(1-\sqrt{y}\right)}\)
1) Giải pt: \(x=\left(2016+\sqrt{x}\right)\left(1-\sqrt{x}\right)\)
2) Giải hpt: \(\left\{{}\begin{matrix}\left(x+2\right)^2+4\left(y-1\right)^2=4xy+13\\\sqrt{\frac{x^2-xy-2y^2}{x-y}}+\sqrt{x+y}=\frac{2}{\sqrt{x^2-y^2}}\end{matrix}\right.\)
