=>12/(x+y-1)-15/(2x-y+3)=15/2 và 12/(x+y-1)-4/(2x-y+3)=28/5
=>x+y-1=22/9; 2x-y+3=-110/19
=>x+y=31/9; 2x-y=-167/19
=>x=-914/513; y=2681/513
giai he phuong trinh \(\left\{{}\begin{matrix}x+y=1\\x^5+y^5=11\end{matrix}\right.\)
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)
Rút gọn các biểu thức:
a) \(\dfrac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^6}}\) ( a <0 ; b # 0 )
b) \(\sqrt{\dfrac{x-2\sqrt{x}+1}{x+2\sqrt{x}+1}}\) ( x lớn hơn hoặc = 0)
c) \(\sqrt{\dfrac{\left(x-2\right)^2}{\left(3-x\right)^2}}+\dfrac{x^2-1}{x-3}\) ( x<3 tại x = 0,5)
d) \(\dfrac{x-1}{\sqrt{y}-1}.\sqrt{\dfrac{\left(y-2\sqrt{y}+1^2\right)}{\left(x-1\right)^4}}\) ( x # 1; y >= 0, y #1)
e) \(4x-\sqrt{8}+\dfrac{\sqrt{x^3+2x^2}}{\sqrt{x+2}}\) ( x > -2 tại x = -\(\sqrt{2}\))
tim nghiem nguyen duong cua phuong trinh \(\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{7}\)
1. Tìm x để bt có nghĩa
A=\(\dfrac{\sqrt{2x+3}}{\sqrt{x-3}}\)
B=\(\sqrt{\dfrac{2x+3}{x-3}}\)
C=\(\sqrt{-\dfrac{5}{x+2}}\)
D=\(\sqrt{-x}+\dfrac{1}{x+3}\)
2. Rút gọn bt
A=\(\sqrt{\dfrac{a+\sqrt{a^2-1}}{2}}-\sqrt{\dfrac{a-\sqrt{a^2-1}}{2}};\left(a>1\right)\)
B=\(\sqrt{\dfrac{a+\sqrt{a^2-1}}{2}}-\sqrt{\dfrac{a-\sqrt{a^2-b}}{2}};\left(a\ge\sqrt{b};b\ge0\right)\)
C=\(\left(1+\dfrac{a+\sqrt{a}}{a+1}\right)\left(1-\dfrac{a-\sqrt{a}}{\sqrt{a}+1}\right);\left(a\ge0,a\ne1\right)\)
D=\(\dfrac{x^2+\sqrt{x}}{x-\sqrt{x}+1}-\dfrac{2x+\sqrt{x}}{\sqrt{x}};\left(x>0\right)\)
Bài tập: Thực hiện phép tính
\(\left(\dfrac{1}{3}\sqrt{\dfrac{1}{2}}-\dfrac{2}{3}\sqrt{\dfrac{1}{3}}+\dfrac{2}{7}\sqrt{\dfrac{4}{5}}\right):\left(\dfrac{2}{7}\sqrt{\dfrac{1}{8}}\right)\)
Rút gọn các biểu thức sau:
A = \(\dfrac{3}{2\left(2x-1\right)}\sqrt{8\left(4x^2-2x+1\right)x^4}\)
B = \(\dfrac{a-b}{b^2}\sqrt{\dfrac{a^2b^4}{a^2-2ab+b^2}}\)
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) \(\dfrac{x-1}{\sqrt{y}-1}\sqrt{\dfrac{y-2\sqrt{y}+1}{\left(x-1\right)^4}}\left(x\ne1,y\ne1\right),y\ge0\)
