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ta có:
\(1+\frac{1}{4}+\frac{1}{28}+\frac{1}{70}+...+\frac{1}{x\left(x+3\right)}\)=1\(\frac{7}{24}\)\(=\frac{31}{24}\)
\(1+\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{x\left(x+3\right)}=\frac{31}{24}\)
\(3+\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{x\left(x+3\right)}=\frac{31}{3}\)
\(3+1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+3}=\frac{31}{3}\)
\(3+1-\frac{1}{x+3}=\frac{31}{3}\)
\(4-\frac{1}{x+3}=\frac{31}{3}\)
\(\frac{1}{x+3}=4-\frac{31}{3}=\frac{-19}{3}\)
=>ko tìm được x
\(a,5x-114=386\\ \Leftrightarrow5x=500\\ \Leftrightarrow x=100\\ b,x\cdot\left(12\cdot4-2\cdot18\right)=612\\ \Leftrightarrow x\cdot\left(48-36\right)=612\\ \Leftrightarrow x\cdot12=612\\ \Leftrightarrow x=51\)
c, x : 27 = 23 dư 9
⇒ \(x=23\cdot27+9\\\Leftrightarrow x=630\)
\(5^{x-1}-13=612\)
\(\Leftrightarrow5^{x-1}=625\)
\(\Leftrightarrow5^{x-1}=5^4\)
\(\Leftrightarrow x-1=4\)
\(\Leftrightarrow x=5\)
5x - 13 = 612
5x = 612 + 13
5x = 625
x = 625 : 5
x = 125
Vậy x = 125
5x-1-13=612
5x-1=612+13
5x-1=625
5x=625+1
5x=626
x=626:5
x=125,2
5x+3 - 13 = 612
<=> 5x+3 = 625
<=> 5x+3 = 54
<=> x + 3 = 4
<=> x = 1
\(5^x+3-13=162\)
\(\Rightarrow5^x+3=162+13\)
\(\Rightarrow5^x+3=175\)
\(\Rightarrow5^x=175-3\)
\(\Rightarrow5^x=172\)
\(\Rightarrow x\in\varnothing\)
Bài 1:
\(\frac{3}{7}\cdot\frac{9}{2}-\frac{1}{14}\cdot\frac{1}{13}\)=\(\frac{27}{14}-\frac{1}{14}\cdot\frac{1}{13}\)
= \(\frac{1}{14}\left(27-\frac{1}{3}\right)\)
= \(\frac{1}{14}\cdot\frac{350}{13}\)=\(\frac{25}{13}\)
bài 2:\(\frac{5}{9}\cdot\frac{7}{13}+\frac{5}{9}\cdot\frac{9}{13}\cdot\frac{3}{13}\)= \(\frac{5}{9}\cdot\frac{1}{13}\left(7+9\cdot\frac{3}{13}\right)\)
= \(\frac{5}{9}\cdot\frac{1}{13}\cdot\frac{94}{13}\)=\(\frac{470}{1521}\)
có j sai xin mn chỉ bảo!
5x-1 -13 = 612
5x-1 =612+13
5x-1 =625
5x-1 =54
=>x-1=4
x=4+1
x=5