Hỏi nữa
Tìm các giá trị của x để các biểu thức sau đây nhận giá trị âm:
a/\(x^2+2006x\)
b/\(3\left(2x-5\right)\left(3x-\frac{5}{3}\right)\)
1.Tìm x :
a,\(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{x\left(x+1\right)}=\frac{13}{90}\)
b,\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{x\left(x+3\right)}=\frac{49}{148}\)
c,\(\frac{7}{\left(x+3\right)\left(x+10\right)}+\frac{11}{\left(x+10\right)\left(x+21\right)}\)\(+\frac{1}{\left(x+21\right)\left(x+34\right)}=\frac{x}{\left(x+3\right)\left(x+34\right)}\)
d,\(\frac{3}{\left(x-4\right)\left(x-7\right)}+\frac{6}{\left(x-7\right)\left(x-13\right)}\)\(+\frac{15}{\left(x-13\right)\left(x-28\right)}\)\(-\frac{1}{x-38}=\frac{-1}{20}\)
Tìm GTNN của biểu thức:
a) \(\left|x+5\right|+\left|x+17\right|\)
b) \(\left|x+8\right|+\left|x+13\right|+\left|x+50\right|\)
c) \(\left|x+5\right|+\left|x+2\right|+\left|x-7\right|+\left|x-8\right|\)
d) \(\left|x+3\right|+\left|x-2\right|+\left|x-5\right|\)
Tìm x
\(\left|2x-5\right|+\left|20-8x\right|=100\)
\(\dfrac{2}{\left(x-1\right)\left(x-3\right)}\)+\(\dfrac{2}{\left(x-3\right)\left(x-8\right)}+\dfrac{12}{\left(x-8\right)\left(x-20\right)}-\dfrac{1}{x-20}=\dfrac{-3}{4}\)
Tính giá trị các biểu thức sau:
\(a,A=-a+\left(b-d\right)-\left(c+a\right)-\left(b-a\right)\)
\(b,B=d-\left(a+c\right)+\left(b+d\right)-b+\left(b-c\right)\)
CMR với mọi số hữu tỉ x;y thì:
a)\(\left|x+y\right|\le\left|x\right|+\left|y\right|\)
b) \(\left|x-y\right|\ge\left|x\right|+\left|y\right|\)
Cho \(A=\left(-7\right)+\left(-7\right)^2+\left(-7\right)^3+...+\left(-7\right)^{2007}\)
Chứng minh rằng : \(A⋮43\)
a) 12,5.\(\left(-\dfrac{5}{7}\right)+1,5.\left(-\dfrac{5}{7}\right)\)
b) \(\left(-\dfrac{2}{5}-\dfrac{3}{7}\right):\dfrac{4}{5}+\left(-\dfrac{1}{5}+\dfrac{3}{7}\right);\dfrac{4}{5}\)
c) \(12.\left(-\dfrac{2}{3}\right)^2+\dfrac{4}{3}\)
d) \(1:\left(\dfrac{2}{3}-\dfrac{3}{4}\right)^2\)
e) \(15.\left(-\dfrac{2}{3}\right)^{^{ }2}-\dfrac{7}{3}\)
f) \(\dfrac{5^4.20^4}{25^5.4^5}\)
