a: ta có: A>0
=>x(x+4)>0
=>x>0 hoặc x<-4
b: Ta có: B>0
=>(x-3)(x+7)>0
=>x>3 hoặc x<-7
c: Ta có: C>0
\(\Leftrightarrow x^2\cdot\dfrac{1}{6}>0\)
hay x<>0
d: ta có: D<0
\(\Leftrightarrow x\left(x-\dfrac{2}{5}\right)< 0\)
=>0<x<2/5
e: Ta có: E<0
\(\Leftrightarrow\dfrac{x-2}{x-6}< 0\)
=>2<x<6
Tìm giá trị lớn nhất hoặc nhỏ nhất của biểu thức sau
a, A = \(2x^2-2\)
b, B = \(\left|x+\dfrac{1}{3}\right|-\dfrac{1}{6}\)
c, C = \(\dfrac{\left|x\right|+2017}{2018}\)
d, D = \(3-\left(x+1\right)^2\)
e, E = \(-\left|0,1+x\right|-1,9\)
f, F = \(\dfrac{1}{\left|x\right|+2017}\)
Tìm x, y, z:
a) \(\left|x+\dfrac{19}{5}\right|+\left|y+\dfrac{1890}{1975}\right|+\left|z-2005\right|=0\)
b) \(\left|x+\dfrac{3}{4}\right|+\left|y-\dfrac{1}{5}\right|+\left|x+y+z\right|\) = 0
c) \(\dfrac{16}{2^x}=1\)
d) \(\left(2x-1\right)^3=-27\)
e) \(\left(x-2\right)^2=1\)
f) \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{4}{25}\)
g) \(\left(x-1\right)^2=\left(x-1\right)^6\)
1 tính
a, \(-\dfrac{2}{3}-\left(\dfrac{-2}{5}\right)-\dfrac{7}{10}\)
b, \(\dfrac{-5}{9}.\left(\dfrac{3}{10}-\dfrac{2}{5}\right)\)
c, \(\left(\dfrac{11}{24}:\dfrac{55}{36}\right).\dfrac{10}{3}\)
d, \(\left(\dfrac{1}{2}-1\right).\left(\dfrac{1}{3}-1\right)...\left(\dfrac{1}{2017}-1\right)\)
e,\(\left(\dfrac{2}{3}\right):\left(\dfrac{4}{9}\right)^{10}\)
f,\(\left(\dfrac{1}{7}\right)^7.7^7\)
g, \(\dfrac{\left(125\right)^5}{5^{15}}\)
2 tìm x, biết
a, \(\dfrac{-4}{7}-x=\dfrac{5}{7}\)
b, \(x:\left(\dfrac{-3}{8}\right)=\dfrac{1}{2}\)
c, \(\dfrac{-3}{5}+\dfrac{1}{4}:x=\dfrac{-2}{5}\)
d, \(\left(x-\dfrac{2}{5}\right).\left(x+\dfrac{3}{7}\right)=0\)
e, \(\left(x+1\right)^5=-32\)
f, \(x-\left(1,5-7\right)=0,35\)
3 tìm số tự nhiên n biết
a, \(3^n=81\)
b, \(2^n=16\)
c, \(2.2^n=16\)
d, \(2.8^n=128\)
5 so sánh
a, \(2^{333}\) và \(3^{222}\)
b, \(\left(\dfrac{-1}{16}\right)^{100}\) và \(\left(\dfrac{-1}{2}\right)^{400}\)
tìm x;y
b \(\left|x-y\right|+\left|y+\dfrac{9}{25}=0\right|\)
c \(\left(\dfrac{1}{2}x-5\right)^{20}+\left(y^2-\dfrac{1}{4}\right)^{10}=0\)
a \(\left|\dfrac{1}{2}-\dfrac{1}{3}+x\right|=\dfrac{-1}{4}-y\)
d \(\left|x\left(x^2-\dfrac{5}{4}\right)\right|=x\) \(\left(x\ge0\right)\)
e \(x^2+\left(y-\dfrac{1}{10}\right)^4=0\)
tìm x biết
a) \(\dfrac{1}{2}x+2\dfrac{1}{2}=3\dfrac{1}{2}x-\dfrac{3}{4}\)
b) \(\dfrac{2}{3}x-\dfrac{2}{5}=\dfrac{1}{2}x-\dfrac{1}{3}\)
c) \(\dfrac{1}{3}x+\dfrac{2}{5}\left(x+1\right)=0\)
d) \(\dfrac{2}{3}-\dfrac{1}{3}\left(x-\dfrac{3}{2}\right)-\dfrac{1}{2}\left(2x+1\right)=5\)
e) \(\dfrac{x+2015}{5}+\dfrac{x+2016}{4}=\dfrac{x+2017}{3}+\dfrac{x+2018}{2}\)
a, cho A = \(\dfrac{\sqrt{x+1}}{\sqrt{x-3}}\). tìm x để A có giá trị nguyên ( x ϵ Z)
b, Thực hiện phép tính: {[(2\(\sqrt{2}\))\(^2\) : 2,4] x [5,25 : (\(\sqrt{7}\))\(^2\)]} : {[2\(\dfrac{1}{7}\) : \(\dfrac{\left(\sqrt{5}\right)^2}{7}\)] : [2\(^2\) : \(\dfrac{\left(2\sqrt{2}\right)^2}{\sqrt{81}}\)]}
1)Tính giá trị biểu thức:
\(\dfrac{\left(13\dfrac{1}{4}-2\dfrac{5}{27}-10\dfrac{5}{6}\right).230\dfrac{1}{25}+46\dfrac{3}{4}}{\left(1\dfrac{3}{7}+\dfrac{10}{3}\right):\left(12\dfrac{1}{3}-14\dfrac{2}{7}\right)}\)
2)Tìm x biết:
a) \(42+\dfrac{3}{7}.\left|3x-1\right|=12\)
b) \(\left|2x-1\right|=\left|x+2\right|\)
c) \(2.3^x.3^2=18\) với \(x\in N\)
Bài 1: Cho tỉ lệ thức \(\dfrac{a}{b}=\dfrac{c}{d}\). Chứng minh
a) \(\dfrac{a+c}{c}=\dfrac{b+d}{d}\)
b) \(\dfrac{a+c}{b+d}=\dfrac{a-c}{b-d}\)
c) \(\dfrac{a-c}{a}=\dfrac{b-d}{b}\)
d) \(\dfrac{3a+5b}{2a-7b}=\dfrac{3c+5d}{2c-7d}\)
e) \(\dfrac{\left(a+b\right)^2}{\left(c-d\right)^2}=\dfrac{ab}{cd}\)
f) \(\left(\dfrac{a-b}{c-d}\right)^{2012}=\dfrac{a^{2012}+b^{2012}}{c^{2012}+d^{2012}}\)
Bài 2: Tìm x, biết
a) \(\dfrac{3}{x-4}=\dfrac{x+4}{3}\)
b) \(\dfrac{x+2}{2}=\dfrac{1}{1-x}\)
c) \(\dfrac{x+7}{x+4}=\dfrac{x-1}{x-2}\)
Bài 3: Cho tỉ lệ thức \(\dfrac{3x-y}{x+y}=\dfrac{3}{4}\)
Tìm giá trị của tỉ số \(\dfrac{x}{y}\)
Tìm x
a) \(\left(\dfrac{3}{5}x-\dfrac{2}{3}x-x\right)\cdot\dfrac{1}{7}=-\dfrac{5}{21}8\)
b) \(\left(5x-1\right)\cdot\left(2x+\dfrac{1}{3}\right)=0\)
c) \(\dfrac{5\left|x+1\right|}{2}=\dfrac{90}{\left|x+1\right|}\)
