tim 2 so biet
(x+1/2)+(x+1/4)+(x+1/8)+(1/16)
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12x/6 + 4x/6 - 3x/6 = 3/8 - 1/4 - 1/6
13x/6 = (9 - 6 - 4)/24 = -1/24
--> x = -1/52
\(\frac{1}{2}-\left(\frac{1}{3}+\frac{3}{4}\right)\le x\le\frac{1}{24}-\left(\frac{1}{8}-\frac{1}{3}\right)\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}-\frac{3}{4}\le x\le\frac{1}{24}-\frac{1}{8}-\frac{1}{3}\)
\(\Rightarrow\frac{6-4-3}{12}\le x\le\frac{1-3-8}{24}\)
\(\Rightarrow\frac{-1}{12}\le x\le\frac{-10}{24}\)
\(\Rightarrow\frac{-2}{24}\le x\le\frac{-10}{24}\)
\(\Rightarrow-2\le x\le-10\)
\(\Rightarrow x\in\left\{-3;-4;-5;......;-10\right\}\)
a)
\(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+2010\right)=2029099\\ 2011.x+\left(1+2+3+...+2010\right)=2029099\\ 2011.x+2021055=2029099\\ 2011.x=2029099-2021055\\ 2011.x=8044\\ x=8044:2011\\ x=4\)
b)
\(2+4+6+...+2x=210\\ 2.\left(1+2+3+...+x\right)=210\\ 1+2+3+...+x=210:2\\ 1+2+3+...+x=105\\ \dfrac{x.\left(x+1\right)}{2}=105\\ x.\left(x+1\right)=105.2\\ x\left(x+1\right)=210\\ x.\left(x+1\right)=14.15\\\Rightarrow x=14\)
a) x+(x+1)+(x+2)+...+(x+2010)=2029099
x+x+1+x+2+...+x+2010=2029099
2011x+[(2010+1).2010:2]=2029099
2011x+2021055=2029099
2011x=2029099-2021055
2011x=8044
x=8044:2011
x=4
Vậy x=4.
b) 2+4+6+8+...+2x=210
(2x+2)*14:2=210
(2x+2)*7=210
2x+2=210:7
2x+2=30
2x=30-2
2x=28
x=28:2
x=14
Vậy x=14.
x . 4 + 15/16 = 1
x . 4 = 1 – 15/16 = 1/16
x = 1/16 : 4 = 1/64
\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)\)
\(=4x+\left(\frac{8}{16}+\frac{4}{16}+\frac{2}{16}+\frac{1}{16}\right)\)
\(=4x+\frac{15}{16}\)