Tính rồi so A và B :
\(A=\left(0,25\right)^{-1}.\left(1\dfrac{1}{4}\right)^2+25\left[\left(\dfrac{4}{3}\right)^{-2}:\left(1,25\right)^3\right]:\left(\dfrac{-2}{3}\right)^{-3}\)
\(B=\left(0,2\right)^{-3}.\left[\left(\dfrac{-1}{5}\right)^{-2}\right]^{-1}+\left[\left(\dfrac{1}{2}\right)^{-3}\right]^{-2}:\left(\dfrac{1}{8}\right)^{-1}-\left(2^{-3}\right)^{-2}:\dfrac{1}{2^6}\)
Tính nhanh giá trị của các biểu thức sau:
a) \(A=85^2+75^2+65^2+55^2-45^2-35^2-25^2-15^2\)
b) \(B=1^2-2^2+3^2-4^2+5^2-6^2+...+2011^2-2012^2\)
c) \(C=\dfrac{1}{1975}\left(\dfrac{2}{1945}-1\right)-\dfrac{1}{1945}\left(1-\dfrac{2}{1975}\right)-\dfrac{1974}{1975}.\dfrac{1946}{1945}-\dfrac{3}{1975.1945}\)
d) \(D=\left(2^9+2^7+1\right)\left(2^{23}-2^{21}+2^{19}-2^{17}+2^{14}-2^{10}+2^9-2^7+1\right)\)
Thực hiện phép tính các đa thức sau
a) \(\left(3x^2-2x+5\right)\left(2x^2-3x+1\right)\)
b) \(\left(\dfrac{3}{2}x^2-\dfrac{2}{3}x-\dfrac{5}{3}\right)\left(4x^2-\dfrac{3}{2}x-3\right)\)
c) \(\left(\dfrac{3}{4}x^2+2x-\dfrac{1}{3}\right)\left(4x^2-\dfrac{3}{2}x-3\right)\)
d) \(\left(-\dfrac{1}{3}+2x-x^2\right)\left(-2x^2-\dfrac{1}{2}x+2\right)\)
e) \(\left(3xy+\dfrac{1}{2}x\right)\left(3x^{2y}-3xy^2-1\right)\)
1, Tính
a) \(\dfrac{3x^2-5}{x^2-5x}+\dfrac{5-15x}{5x-25}\)
b) \(\dfrac{4+x^3}{x-3}-\dfrac{2x+2x^2}{x-3}+\dfrac{2x-13}{x-3}\)
c) \(\dfrac{2}{x-5}+\dfrac{x-25}{\left(x+5\right)\left(x-5\right)}\)
d) \(\dfrac{2x+8}{x^2-12+1}+\dfrac{7}{x-2}\)
2. Tính giá trị biểu thức
A= \(2\left(x+1\right)+\left(3x+2\right)\left(3x-2\right)-9x^2\)
tại \(x=15\)
Rút gọn \(\left[\dfrac{x}{2x-6}-\dfrac{x^2}{x^2-9}+\dfrac{x}{2x-9}.\left(\dfrac{3}{x}-\dfrac{1}{x-3}\right)\right]:\dfrac{x^2-5x-6}{18-2x^2}\)
Cho biểu thức A= \(\left(\dfrac{x^2-16}{x-4}-1\right):\left(\dfrac{x-2}{x-3}+\dfrac{x+3}{x+1}+\dfrac{x+2-x^2}{x^2-2x-3}\right)\)
1, Rút gọn biểu thức A.
2, Tìm số nguyên x để \(\dfrac{A}{x^2+x+1}\) nhận giá trị nguyên.
Tính:
S= \(\dfrac{\left(1^4+\dfrac{1}{4}\right).\left(3^4+\dfrac{1}{4}\right)......\left(19^4+\dfrac{1}{4}\right)}{\left(2^4+\dfrac{1}{4}\right).\left(4^4+\dfrac{1}{4}\right)......\left(20^4+\dfrac{1}{4}\right)}\)
Tính :
S= \(\dfrac{\left(1^4+\dfrac{1}{4}\right).\left(3^4+\dfrac{1}{4}\right)......\left(19^4+\dfrac{1}{4}\right)}{\left(2^4+\dfrac{1}{4}\right).\left(4^4+\dfrac{1}{4}\right).......\left(10^4+\dfrac{1}{4}\right)}\)
a.\(\dfrac{x+6}{5}-\dfrac{x-2}{3}< 2\)
b. \(\dfrac{x+5}{4}-\dfrac{x^{2^{ }}-3}{6}\ge1-\dfrac{2x^{2^{ }}-1}{12}\)
c. \(x^{2^{ }}-4x+3>0\)
d. \(x^{3^{ }}-2x^{2^{ }}+3x-2\ge0\)
e. \(\left|x+1\right|+\left|x-2\right|=4\)
f. \(\dfrac{5x-1}{10}+\dfrac{2x+3}{6}>\dfrac{x-8}{15}-\dfrac{x-1}{30}\)
h.\(\dfrac{10x+3}{12}< \dfrac{15-8x}{9}\)
