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\(1,A=\dfrac{2}{3\cdot7}+\dfrac{2}{7\cdot11}+\dfrac{2}{11\cdot15}+...+\dfrac{2}{99\cdot103}\\ 2A=\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+\dfrac{4}{11\cdot15}+...+\dfrac{4}{99\cdot103}\\ 2A=\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{99}-\dfrac{1}{103}\\ 2A=\dfrac{1}{3}-\dfrac{1}{103}=\dfrac{100}{309}\\ A=\dfrac{100}{309}\cdot\dfrac{1}{2}=\dfrac{50}{309}\)
\(2,A=\dfrac{7}{2}+\dfrac{7}{6}+\dfrac{7}{12}+\dfrac{7}{20}+\dfrac{7}{30}+\dfrac{7}{42}+\dfrac{7}{56}+\dfrac{7}{72}+\dfrac{7}{90}\\ A=7\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{9\cdot10}\right)\\ A=7\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ A=7\left(1-\dfrac{1}{10}\right)=7\cdot\dfrac{9}{10}=\dfrac{63}{10}\)
\(\left(\frac{505}{707}+\frac{222}{333}\right)\cdot x=\frac{404}{909}\)
=> \(\left(\frac{5}{7}+\frac{2}{3}\right)\cdot x=\frac{4}{9}\)
=> \(\frac{29}{21}\cdot x=\frac{4}{9}\)
=> \(x=\frac{4}{9}:\frac{29}{21}\)
=> \(x=\frac{28}{87}\)
TK mk nha!
( 505/707+ 222/333) . x = 404/ 909
29/21 . x = 4/9
x= 4/9 : 29/21
x= 4/9 . 21/29
x= 28/87
Vậy x= 28/87
Ta có :\(\frac{230+x}{505+x}=\frac{4}{5}\)
\(\Rightarrow5.\left(230+x\right)=4.\left(505+x\right)\)
\(\Rightarrow1150+5x=2020+4x\)
\(\Rightarrow5x-4x=2020-1150\)
\(\Rightarrow x=870\)
Vậy x =870
Khi y \(\ge3\) => 2x < 0 => x \(\in\varnothing\)
=> y < 3
=> y \(\in\left\{0;1;2\right\}\)
Khi y = 2 => 2x = 64 => x = 7
Khi y = 1 => 2x = 484 => x \(\in\varnothing\)
Khi y = 0 => 2x =504 => x \(\in\varnothing\)
Vậy x = 7 ; y = 2
\(Khi\text{ y}\ge3\Rightarrow2^x< 0\Rightarrow x\in\varnothing\)
\(\Rightarrow y< 3\)
\(\Rightarrow y\in\left\{0;1;2\right\}\)
\(Khi\text{ y}=2\Rightarrow2^x=64\Rightarrow x=7\)
\(Khi\text{ y}=1\Rightarrow2^x=484\Rightarrow x\in\varnothing\)
\(Khi\text{ y}y=0\Rightarrow2^x=504\Rightarrow x\in\varnothing\)
\(\text{Vậy x=7;y=2}\)
\(\text{Hok tốt!}\)
\(\text{@Kaito Kid}\)
a) (x – 45).27 = 0 ó x – 45 = 0 ó x = 45
b) 41.(2x – 8).13 = 0 ó 2x – 8 = 0 ó x = 4
c) (x – 36):18 = 12 ó x – 36 = 12.18 ó x = 216 + 36 ó x = 252
d) 43.(x – 18) = 86 ó x – 18 = 86:43 ó x = 2+18 ó x = 20
e) 96 : (121 – x) = 4 ó 121 – x = 96 : 4 ó 121 – x = 24 ó x = 121 – 24 ó x = 97
f) 340 : (15x+5) = 17 ó 15x + 15 = 340 :17 ó 15x + 5 = 20 ó 15x = 20 – 5 ó 15x = 15 ó x = 1