3+2.|x-2|=23-(-1)
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7 tháng 8 2019
\(1,\frac{2}{3}+\frac{4}{9}+\frac{1}{5}+\frac{2}{15}+\frac{3}{2}-\frac{17}{18}\)
\(< =>\frac{4}{9}+\frac{3}{2}+\left(\frac{2}{3}+\frac{1}{5}+\frac{2}{15}\right)-\frac{17}{18}\)
\(< =>\frac{8}{18}+\frac{27}{18}+\left(\frac{10}{15}+\frac{3}{15}+\frac{2}{15}\right)-\frac{17}{18}\)
\(< =>\frac{35}{18}+1-\frac{17}{18}\)
\(< =>\frac{53}{18}-\frac{17}{18}\)
\(< =>2\)
\(2,\frac{13}{28}\cdot\frac{5}{12}-\frac{5}{28}\cdot\frac{1}{12}\)
\(< =>\left(\frac{13}{28}-\frac{5}{28}\right)\cdot\left(\frac{5}{12}-\frac{1}{12}\right)\)
\(< =>\frac{2}{7}\cdot\frac{1}{3}\)
\(< =>\frac{2}{21}\)
\(3,\frac{19}{4}\cdot\frac{15}{23}-\frac{15}{4}\cdot\frac{7}{23}+\frac{15}{4}\cdot\frac{11}{23}\)
\(< =>\frac{285}{92}-\frac{105}{92}+\frac{165}{92}\)
\(< =>\frac{15}{4}\)
17 tháng 2 2020
\(\frac{x-23}{24}+\frac{x-23}{25}=\frac{x-23}{26}\)
\(\Leftrightarrow\frac{x-23}{24}+\frac{x-23}{25}-\frac{x-23}{26}=0\)
\(\Leftrightarrow\left(x-23\right)\left(\frac{1}{24}+\frac{1}{25}-\frac{1}{26}\right)=0\)
\(\Leftrightarrow x-23=0\left(vì\frac{1}{24}+\frac{1}{25}-\frac{1}{26}\ne0\right)\)
\(\Leftrightarrow x=23\)
vậy................
\(\frac{201-x}{99}+\frac{203-x}{97}+\frac{205-x}{95}+3=0\)
\(\Leftrightarrow\left(\frac{201-x}{99}+1\right)+\left(\frac{203-x}{97}+1\right)+\left(\frac{205-x}{95}+1\right)=0\)
\(\Leftrightarrow\frac{300-x}{99}+\frac{300-x}{97}+\frac{300-x}{95}=0\)
\(\Leftrightarrow\left(300-x\right)\left(\frac{1}{99}+\frac{1}{97}+\frac{1}{95}\right)=0\)
\(\Leftrightarrow300-x=0\left(vì\frac{1}{99}+\frac{1}{97}+\frac{1}{95}>0\right)\)
\(\Leftrightarrow x=300\)
vậy..........
H9
HT.Phong (9A5)
CTVHS
9 tháng 7 2023
a) Đặt: \(A=1+2^2+2^3+...+2^{10}\)
\(\Rightarrow2A=2\left(1+2^2+2^3+...+2^9+2^{10}\right)\)
\(\Rightarrow2A=2+2^3+2^4+...+2^{10}+2^{11}\)
\(\Rightarrow2A-A=\left(2+2^3+2^4+...+2^{10}+2^{11}\right)-\left(1+2^2+2^3+...+2^{10}\right)\)
\(\Rightarrow A=\left(2^3-2^3\right)+\left(2^4-2^4\right)+...+\left(2-1\right)+\left(2^{11}-2^2\right)\)
\(\Rightarrow A=0+0+...+1+\left(2^{11}-2^2\right)\)
\(\Rightarrow A=1+2^{11}-2^2=1+2048-4=2045\)
Vậy: \(1+2^2+2^3+...+2^{10}=2045\)
b)
a] \(60-3\left(x-1\right)=2^3\cdot3\)
\(\Rightarrow60-3\left(x-1\right)=24\)
\(\Rightarrow3\left(x-1\right)=36\)
\(\Rightarrow x-1=12\)
\(\Rightarrow x=13\)
b] \(\left(3x-2\right)^3=2\cdot2^5\)
\(\Rightarrow\left(3x-2\right)^3=2^6\)
\(\Rightarrow\left(3x-2\right)^3=\left(2^2\right)^3\)
\(\Rightarrow3x-2=2^2\)
\(\Rightarrow3x=6\)
\(x=2\)
c] \(5^{x+1}-5^x=500\)
\(\Rightarrow5^x\left(5-1\right)=500\)
\(\Rightarrow5^x\cdot4=500\)
\(\Rightarrow5^x=125\)
\(\Rightarrow5^x=5^3\)
\(\Rightarrow x=3\)
d] \(x^2=x^4\)
\(\Rightarrow x=x^2\)
\(\Rightarrow x-x^2=0\)
\(\Rightarrow x\left(1-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\1-x=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
22 tháng 8 2018
1. Tính:
a) 23 + 24 - ( 65 x 2 - 4 ) x 4 + 66 + 44 - ( 54 : 9 x 9 : 9 + 45 ) : 1 + 1 - 1 x ( 23 + 23 - 23 x 2 +1 ) = 51
b) 4444444444444444444444444444444444444444444444444444444444444444444 : 1
= 4444444444444444444444444444444444444444444444444444444444444444444
c) 30 = 0
d) 1/1 = 1
e)
22 tháng 8 2018
a) - 530
b) 44444444444444444444444444444444444444444444444444444444444444444444
c) 0
d) 1
e) Em là em
\(3+2\left|x-2\right|=2^3-\left(-1\right)\)
\(\Rightarrow3+2\left|x-2\right|=8+1\)
\(\Rightarrow2\left|x-2\right|=9-3\)
\(\Rightarrow2\left|x-2\right|=6\)
\(\Rightarrow\left|x-2\right|=6\div2\)
\(\Rightarrow\left|x-2\right|=3\)
\(\Rightarrow\orbr{\begin{cases}x-2=-3\\x-2=3\end{cases}}\)
\(\text{Trường hợp : }x-2=-3\)
\(\Rightarrow x=-3+2\)
\(\Rightarrow x=-1\)
\(\text{Trường hợp : }x-2=3\)
\(\Rightarrow x=3+2\)
\(\Rightarrow x=5\)
\(\text{Vậy }x\in\left\{-1;5\right\}\)
\(3+2.\left|x-2\right|=2^3-\left(-1\right)\)
\(\Leftrightarrow3+2.\left|x-2\right|=2^3+1\)
\(\Leftrightarrow3+2.\left|x-2\right|=8+1\)
\(\Leftrightarrow3+2.\left|x-2\right|=9\)
\(\Leftrightarrow2.\left|x-2\right|=9-3\)
\(\Leftrightarrow2.\left|x-2\right|=6\)
\(\Leftrightarrow\left|x-2\right|=6:2\)
\(\Leftrightarrow\left|x-2\right|=3\)
Xét 2 TH:
TH1:
x - 2 = -3
x = -3 + 2
x = -1
TH2:
x - 2 = 3
x = 3 + 2
x = 5
\(\Rightarrow\orbr{\begin{cases}x=-1\\x=5\end{cases}}\)