(3/1/2-0,5)x1/27+1/1/3
(làm luôn hộ mình nhá)
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4/5 + 3/4 : X = 1/2
3/4:x = 1/2 - 4/5
3/4 : x = -3/10
x=3/4 : (-3/10)
x=-5/2
\(a;\left|1-2x\right|=3\)
\(\Leftrightarrow\left|2x-1\right|=3\Leftrightarrow2x-1=\pm3\)
\(\Leftrightarrow\orbr{\begin{cases}2x-1=3\\2x-1=-3\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=4\\2x=-2\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=4:2=2\\x=\left(-2\right):2=-1\end{cases}}}\)
Vậy x=2;-1
\(b;\left(x+1\right)\left(1-5x\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+1=0\\1-5x=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-1\\5x=1\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=-1\\x=\frac{1}{5}\end{cases}}}\)
#)Giải :
\(A=1+2+2^2+...+2^{100}\)
\(2A=2+2^2+2^3+...+2^{101}\)
\(2A-A=\left(2+2^2+2^3+...+2^{101}\right)-\left(1+2+2^2+...+2^{100}\right)\)
\(A=2^{101}-1\)
\(B=1+3^2+3^4+...+3^{100}\)
\(3^2B=3^2+3^4+3^6+...+3^{102}\)
\(3^2B-B=\left(3^2+3^4+3^6+...+3^{102}\right)-\left(1+3^2+3^4+...+3^{100}\right)\)
\(8B=3^{102}-1\)
\(B=\frac{3^{102}-1}{8}\)
\(C=1+5^3+5^6+...+5^{99}\)
\(5^2C=5^3+5^6+5^9+...+5^{102}\)
\(5^2C-C=\left(5^3+5^6+5^9...+5^{102}\right)-\left(1+5^3+5^6+...+5^{99}\right)\)
\(24C=5^{102}-1\)
\(C=\frac{5^{102}-1}{24}\)
a) A = 1 + 22 + ... + 2100
=> 2A = 22 + 23 + ... + 2101
Lấy 2A - A = (2 + 22 + ... + 2101) - (1 + 22 + ... 2100)
A = 2101 - 1
b) B = 1 + 32 + 34 + ... + 3100
=> 32B = 32 + 34 + 36 + ..... + 3102
=> 9B = 32 + 34 + 36 + ..... + 3102
Lấy 9B - B = ( 32 + 34 + 36 + ..... + 3102) - (1 + 32 + 34 + ... + 3100)
8B = 3102 - 1
B = \(\frac{3^{102}-1}{8}\)
c) C = 1 + 53 + 56 + ... + 599
=> 53.C = 53 . 56 . 59 + ... + 5102
=> 125.C = 53 . 56 . 59 + ... + 5102
Lấy 125.C - C = (53 . 56 . 59 + ... + 5102) - (1 + 53 + 56 + ... + 599)
124.C = 5102 - 1
=> C = \(\frac{5^{102}-1}{124}\)
\(A=\left(-0,5-\frac{2}{3}\right):\left(-3\right)+\left(-1,6\right):\left(-2\right)\)
\(A=\left(-\frac{1}{2}-\frac{2}{3}\right):\left(-\frac{3}{1}\right)+\left(-\frac{1}{6}\right):\left(-\frac{2}{1}\right)\)
\(A=\left(\frac{-3}{6}-\frac{4}{6}\right):\left(-\frac{3}{1}\right)+\left(-\frac{1}{6}\right).\left(-\frac{1}{2}\right)\)
\(A=\left(-\frac{7}{6}\right).\left(-\frac{1}{3}\right)+\frac{1}{12}\)
\(A=\frac{7}{18}+\frac{1}{12}\)
\(A=\frac{14}{36}+\frac{3}{36}\)
\(A=\frac{17}{36}\)
\(\left(3\frac{1}{2}-0,5\right)x\frac{1}{27}+1\frac{1}{3}\)
= \(3x\frac{1}{27}+1\frac{1}{3}\)
= \(\frac{1}{9}+\frac{4}{3}\)
= \(\frac{13}{9}\)