\(\dfrac{5+x}{4-x}=\dfrac{1}{2}\)
\(\dfrac{25}{14}=\dfrac{x+7}{x-4}\)
\(\dfrac{3x-5}{x+4}=\dfrac{5}{2}\)
\(\dfrac{3x-1}{2x+1}=\dfrac{3}{7}\)
Tính giá trị của các biểu thức sau
1) \(A=1+2+2^2+...+2^{2015}\)
2) \(B=\left(\dfrac{1}{4}-1\right)\cdot\left(\dfrac{1}{9}-1\right)\cdot\left(\dfrac{1}{16}-1\right)\cdot\cdot\cdot\cdot\cdot\left(\dfrac{1}{400}-1\right)\)
3) \(C=\left(\dfrac{1}{4\cdot9}+\dfrac{1}{9\cdot14}+\dfrac{1}{14\cdot19}+...+\dfrac{1}{44\cdot49}\right)\cdot\dfrac{1-3-5-7-...-49}{89}\)
4) \(D=\dfrac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6+8^4\cdot3^5}-\dfrac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\)
5) \(E=\dfrac{\dfrac{1}{2003}+\dfrac{1}{2004}-\dfrac{1}{2005}}{\dfrac{5}{2003}+\dfrac{5}{2004}-\dfrac{5}{2005}}-\dfrac{\dfrac{2}{2002}+\dfrac{2}{2003}-\dfrac{2}{2004}}{\dfrac{3}{2002}+\dfrac{3}{2003}-\dfrac{3}{2004}}\)
6) Cho 13+23+...+103=3025
Tính S= 23+43+63+...+203
\(5\dfrac{8}{1}+1\dfrac{8}{7}\)
Tinh
\(\dfrac{0,4-\dfrac{2}{9}+\dfrac{2}{11}}{1,4-\dfrac{7}{9}+\dfrac{7}{11}}-\dfrac{\dfrac{1}{3}-0.25+\dfrac{1}{5}}{1\dfrac{1}{6}-0,875+0,7}\)
\(\dfrac{-9}{46}\)-4\(\dfrac{1}{23}\):(3\(\dfrac{1}{4}\)-x:\(\dfrac{3}{5}\))+2\(\dfrac{8}{23}\)=1
1. Tìm x biết:
(\(\dfrac{-1}{2}\) . x + \(\dfrac{2}{3}\)) . \(\dfrac{-5}{7}\)= \(\dfrac{28}{15}\)
Bài 1: Tính :
F=\(-17,5+\dfrac{5}{3}-2\dfrac{1}{7}\)/\(7-\dfrac{2}{3}+\dfrac{6}{7}\)
Bài 2: Tìm \(n\in Z\) biết :
\(125\le5.5^n\le25\)
Bài 3: So sánh:
\(4^{300}+3^{300}-2^{300}\) và \(3.24^{100}\)
Tính:
\(N=\left(0,25\right)^{-1}\cdot\left(\dfrac{1}{4}\right)^{-2}\cdot\left(\dfrac{4}{3}\right)^{-2}\cdot\left(\dfrac{5}{4}\right)^{-1}\cdot\left(\dfrac{2}{3}\right)^{-3}\)\(N=\left(0,25\right)^{-1}\cdot\left(\dfrac{1}{4}\right)^{-2}\cdot\left(\dfrac{4}{3}\right)^{-2}\cdot\left(\dfrac{5}{4}\right)^{-1}\cdot\left(\dfrac{2}{3}\right)^{-3}\)
Giải các phương trình sau :
a) \(\dfrac{14x-5-8x^2}{3x-1-2x^2}+\dfrac{3-2x}{x-1}=2\)
b) \(\sqrt{x^2-3x+8}+4=x\)
c) \(\sqrt{x^2-5x-2}=8-x\)
d) \(2-\dfrac{3}{3-x}=\dfrac{3-2x}{x^2-7x+12}\)
