\(G=\dfrac{x-\sqrt{x}-2-x-\sqrt{x}+2}{\left(\sqrt{x}+1\right)^2\cdot\left(\sqrt{x}-1\right)}\cdot\dfrac{\left(x-1\right)^2}{2}\)
\(=-\dfrac{2\sqrt{x}\left(\sqrt{x}-1\right)}{2}=-\sqrt{x}\left(\sqrt{x}-1\right)\)
1.Giải hệ phương trình:
\(\left\{{}\begin{matrix}2x+y=5\\3x-2y=11\end{matrix}\right.\)
2.Rút gọn biểu thức:
B=\(\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-2}+\dfrac{2\sqrt{x}}{\sqrt{x}+2}+\dfrac{5\sqrt{x}+2}{4-x}\right):\dfrac{1}{\sqrt{x}+2}\)với x>0;x\(\ne\)9
Giải hệ phương trình :
a) \(\left\{{}\begin{matrix}x^2+y^2=1\\x^2+y^2=1\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}\sqrt{x}+\sqrt{y}+\sqrt{z}=2014\\\dfrac{1}{3x+2y}+\dfrac{1}{3y+2z}+\dfrac{1}{3z+2x}=\dfrac{1}{x+2y+3z}+\dfrac{1}{y+2x+3x}+\dfrac{1}{z+2x+3y}\end{matrix}\right.\)
1.giải hệ phương trình:
\(\left\{{}\begin{matrix}2x-y=3\\x+y=0\end{matrix}\right.\)
2.Rút gọn biểu thức
\(A=\dfrac{x+20}{x-4}+\dfrac{2}{\sqrt{x}+2}-\dfrac{6}{\sqrt{x}-2}\) với x\(\ge\)0;x\(\ne\)4
Cho \(\left\{{}\begin{matrix}x,y,z>0\\xy+yz+zx=1\end{matrix}\right.\)
Tính \(S=x\sqrt{\dfrac{\left(1+y^2\right)\left(1+z^2\right)}{1+x^2}}+y\sqrt{\dfrac{\left(1+z^2\right)+\left(1+x^2\right)}{1+y^2}}+z\sqrt{\dfrac{\left(1+x^2\right)+\left(1+y^2\right)}{1+z^2}}\)
Tìm GTNN của biểu thức:
\(A=\dfrac{x^2}{x+y}+\dfrac{y^2}{y+z}+\dfrac{z^2}{x+z}\)
Biết\(\left\{{}\begin{matrix}x.y.z>0\\\sqrt{xy}+\sqrt{yz}+\sqrt{zx}=1\end{matrix}\right.\)
Rút gọn: P=\(\dfrac{xy-\sqrt{x^2-1}.\sqrt{y^2-1}}{xy+\sqrt{x^2-1}.\sqrt{y^2-1}}\) trong đó \(\left\{{}\begin{matrix}x=\dfrac{1}{2}\left(a+\dfrac{1}{a}\right)\\y=\dfrac{1}{2}\left(b+\dfrac{1}{b}\right)\end{matrix}\right.\).
Cho \(A=\left(\dfrac{x\sqrt{x}-1}{x-\sqrt{x}}-\dfrac{x\sqrt{x}+1}{x+\sqrt{x}}\right):\left(\dfrac{2\left(x-2\sqrt{x}+1\right)}{x-1}\right)\)
Tìm x nguyên để A có giá trị nguyên ĐKXĐ: \(x>0; x\ne1\)
Rút gọn biểu thức :
N=\(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{3\sqrt{x}}{x-\sqrt{x}}\) với x>0,x\(\ne\)1
Giải hệ phương trình:
\(\left\{{}\begin{matrix}x+3y=9\\2x-5y=-4\end{matrix}\right.\)
giải hệ:
a) \(\left\{{}\begin{matrix}\sqrt{x+3y}+\sqrt{x+y}=2\\\sqrt{x+y}+y-x=1\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}x+y+\frac{1}{x}+\frac{1}{y}=4\\x^2+y^2+\frac{1}{x^2}+\frac{1}{y^2}=4\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}\left(x-\frac{1}{y}\right)\left(y+\frac{1}{x}\right)=2\\2x^2y+xy^2-4xy=2x-y\end{matrix}\right.\)
d) \(\left\{{}\begin{matrix}2x^2+xy=y^2-3y+2\\x^2-y^2=3\end{matrix}\right.\)
e) \(\left\{{}\begin{matrix}x^2+y^2+z^2+2xy-xz-zy=3\\x^2+y^2-2xy-xz+zy=-1\end{matrix}\right.\)
f) \(\left\{{}\begin{matrix}x^2-y^2+5x-y+6=0\\x^2+\left(x-y\right)^2=2+\sqrt{6x+7}+2\sqrt{x+y+1}\end{matrix}\right.\)
