Dễ thấy y = 0 không thỏa mãn đề
Có: 3xy + 2y = 2xy(x + y) + y2 = 5
=> 3x + 2 = 2x(x + y) + y
=> 2x2 + 2xy + y - 3x - 2 = 0
=> 2x2 + x - 4x - 2 + 2xy + y = 0
=> (2x + 1)(x - 2 + y) = 0
đến đây dễ r`
giai he phuong trinh \(\left\{{}\begin{matrix}x+y=1\\x^5+y^5=11\end{matrix}\right.\)
giai he phuong trinh \(\left\{{}\begin{matrix}\dfrac{4}{x+y-1}-\dfrac{5}{2x-y+3}=\dfrac{5}{2}\\\dfrac{3}{x+y-1}-\dfrac{1}{2x-y+3}=\dfrac{7}{5}\end{matrix}\right.\)
a, \(\dfrac{\sqrt[]{7-2\sqrt[]{6}}}{\sqrt[]{6}-1}\)
b, 2.|x+y|.\(\sqrt[]{\dfrac{1}{x^2+2xy+y^2}}\) (x+y>0)
c, \(\dfrac{\left(x-5\right)^4}{\left(4-x\right)^2}\)-\(\dfrac{x^2-25}{x-4}\)(x<4)
\(\dfrac{\sqrt{xy^3}.\sqrt{x^2-y^2}}{\sqrt{\left(x+y\right)\left(x^2y^3-xy^4\right)}}\)
Rut gon
a)\(\frac{\left(\sqrt{x}+1\right).\left(x-\sqrt{xy}\right).\left(\sqrt{x}+\sqrt{y}\right)}{\left(x-y\right).\left(\sqrt{x^3}+x\right)}\)
b) \(\frac{\left(2-\sqrt{x}\right)^2-\left(\sqrt{x}+3\right)}{1+2.\sqrt{x}}\)
Rut gon
a)\(\frac{\left(\sqrt{x}+1\right).\left(x-\sqrt{xy}\right).\left(\sqrt{x}+\sqrt{y}\right)}{\left(x-y\right).\left(\sqrt{x^3}+x\right)}\)
b) \(\frac{\left(2-\sqrt{x}\right)^2-\left(\sqrt{x}+3\right)}{1+2.\sqrt{x}}\)
. Làm tính nhân :
a) \(\left(\sqrt{12}-3\sqrt{75}\right).\sqrt{3}\)
b) \(\left(\sqrt{18}-4\sqrt{72}\right).2\sqrt{2}\)
c) \(\left(\sqrt{6}-2\right)\left(\sqrt{6}+7\right)\)
d) \(\left(\sqrt{3}+2\right)\left(\sqrt{3}-5\right)\)
2 . Thực hiện phép tính :
a) \(\left(\sqrt{48}-\sqrt{27}+4\sqrt{12}\right):\sqrt{3}\)
b) \(\left(\sqrt{20}-3\sqrt{45}+6\sqrt{180}\right):\sqrt{5}\)
c) \(\left(2\sqrt{20}-3\sqrt{45}+4\sqrt{80}\right):\sqrt{5}\)
d) \(\left(3\sqrt{24}+4\sqrt{54}-5\sqrt{96}\right):\sqrt{6}\)
e) \(\left(\sqrt{x^2y}-\sqrt{xy^2}\right):\sqrt{xy}\)
f) \(\left(\sqrt{a^3b}+\sqrt{ab^3}-ab\right):\sqrt{ab}\)
g) \(\left(3\sqrt{x^2y}-4\sqrt{xy^2}+5xy\right):\sqrt{xy}\)
h) \(\left(\sqrt{a^3b}+\sqrt{ab^3}-3\sqrt{ab}\right):\sqrt{ab}\)
Rút gọn các biểu thức :
a) \(\sqrt{\dfrac{x-2\sqrt{x}+1}{x+2\sqrt{x}+1}};\left(x\ge0\right)\)
b) \(\dfrac{x-1}{\sqrt{y}-1}\sqrt{\dfrac{\left(y-2\sqrt{y}+1\right)^2}{\left(x-1\right)^4}};\left(x\ne1;y\ne1;y\ge0\right)\)
Rút gọn biểu thức:
a) \(\sqrt{\dfrac{x-2\sqrt{x}-1}{x+2\sqrt{x}+1}}\left(x\ge0\right)\)
b) \(\dfrac{x-1}{\sqrt{y}-1}\sqrt{\dfrac{y-2\sqrt{y}+1}{\left(x-1\right)^4}}\left(x\ne1,y\ne1\right),y\ge0\)
