Tìm GTNN:
a) \(\dfrac{1}{-x^2+2x-4}\)

b) \(\dfrac{12}{12x-4x^2-13}\)

c) \(\dfrac{x^2-4x-4}{x^2-4x+5}\)

d) \(\dfrac{15}{-6x^2-5y^2+10xy-4x+10y-19}\)

e)\(\dfrac{x^2-2011}{4.\left(x^2+1\right)}\)

1) Tìm x, y, z biết rằng x^2+y^2+z^2=xy+yz+xz và x^2011+y^2011+z^2011=3^2012

2) Tính A= (1^4+1/4)(3^4+1/4)(5^4+1/4)....(2011^4+1/4) / (2^4+1/4)(4^4+1/4)(6^4+1/4)....(2012^4+1/4)

tính các dãy số sau:

-1-2+3+4-5-6+7+8-.....-2009-2010+2011

-1-2+3-4-5+6+....-2009+2010-2011

Thực hiện phép tính (1/2+1/3+1/4+1/5+1/6+...+1/2012)/(2011/1+2010/2+2009/3+...+1/2011)

1. Tính

a) 6/5 + 6/35 - 6/125 - 6/2009 - 6/2011 

    7/5 + 7/35 + 7/125 + 7/2009 + 7/2011

b)\(\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)...\left(1-\frac{1}{1998^2}\right)\)

1-1/2+1/3-1/4+1/5-1/6+...+1/2011-1/2012    /      1006-1006/1007-1007/1008-1008/1009-...-2010/2011-2011/2012

1)  (3x-2)/3-2=(4x+1)/42)  (x-3)/4+(2x-1)/3=(2-x)/63)  1/2 (x+1)+1/4 (x+3)=3-1/3 (x+2)4)  (x+4)/5-x+4=x/3-(x-2)/25)  (4-5x)/6=2(-x+1)/2 6)  (-(x-3))/2-2=5(x+2)/4 7)2(2x+1)/5-(6+x)/3=(5-4x)/158)  (7-3x)/2-(5+x)/5=1 9)(x-1)/2+3(x+1)/8=(11-5x)/310)(3+5x)/5-3=(9x-3)/4  

Tính:

B = 1*2+2*3+3*4+...+2011*2012

C =1*50+2*49+3*48+...+49*2+50*1

D = 4*7+7*10+10*13+...+205*208

E = (2+4+6+8+..+2014)-(3+5+7+9+...+2011)

1) (3x-2)/3-2=(4x+1)/4
2) (x-3)/4+(2x-1)/3=(2-x)/6
3) 1/2 (x+1)+1/4 (x+3)=3-1/3 (x+2)
4) (x+4)/5-x+4=x/3-(x-2)/2
5) (4-5x)/6=2(-x+1)/2
6) (-(x-3))/2-2=5(x+2)/4
7)2(2x+1)/5-(6+x)/3=(5-4x)/15
8) (7-3x)/2-(5+x)/5=1
9)(x-1)/2+3(x+1)/8=(11-5x)/3
10)(3+5x)/5-3=(9x-3)/4