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\(120\left(\dfrac{1}{24.25}+\dfrac{1}{25.26}+...+\dfrac{1}{29.30}\right)+x=\dfrac{1}{3}\)
\(\Rightarrow120\left(\dfrac{1}{24}-\dfrac{1}{25}+\dfrac{1}{25}+\dfrac{1}{26}+...+\dfrac{1}{29}-\dfrac{1}{30}\right)+x=\dfrac{1}{3}\)
\(\Rightarrow120\left(\dfrac{1}{24}-\dfrac{1}{30}\right)+x=\dfrac{1}{3}\)
\(\Rightarrow120.\dfrac{1}{120}+x=\dfrac{1}{3}\)
\(\Rightarrow1+x=\dfrac{1}{3}\)
\(\Rightarrow x=-\dfrac{2}{3}\)
2x+ 2x+1+ 2x+2 + 2x+3 = 2x+ 2x.2 + 2x.22 + 2x.23 = 2x(1+ 2 + 22 + 23) = 2x.15 = 120 => 2x =120:15 = 8 => x = 3
2x + 2x+1 +2x+2 + 2x+3 = 120
Suy ra 2x .1 + 2x . 2 + 2x . 22 + 2x . 23 = 120
Suy ra 2x .( 1 + 2 + 4 + 8 ) = 120
Suy ra 2x . 15 = 120
Suy ra 2x = 120 : 15
Suy ra 2x = 8
Suy ra 2x = 23
Do đó x = 3
Vậy x = 3
\(2^x+2^{x+1}+2^{x+2}+2^{x+3}=120\)
\(\Rightarrow2^x+2^x.2+2^x.2^2+2^x.2^3=120\)
\(\Rightarrow2^x+2^x.2+2^x.4+2^x.8=120\)
\(\Rightarrow2^x\left(1+2+4+8\right)=120\)
\(\Rightarrow2^x.15=120\)
\(\Rightarrow2^x=120:15\)
\(\Rightarrow2^x=8\)
\(\Rightarrow2^x=2^3\)
\(\Rightarrow x=3\)
\(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{29\cdot30}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{29}-\dfrac{1}{30}\)
\(=1-\dfrac{1}{30}\)
\(=\dfrac{30}{30}-\dfrac{1}{30}\)
\(=\dfrac{29}{30}\)
Tìm x biết:
\(\frac{x}{2013}-\frac{1}{10}-\frac{1}{15}-\frac{1}{21}-.....-\frac{1}{120}=\frac{5}{8}\)
PT <=> (3x - 1)(6x - 1)(4x - 1)(5x - 1) = 120
. <=> (18x² - 9x + 1)(20x² - 9x + 1) = 120
Đặt a = 19x² - 9x + 1 (Đk a > 0) ta có PT: (a - 1)(a + 1) = 120
<=> a² - 1 = 120
<=> a² = 121
<=> a = 11 (Vì a >0)
Với a = 11 ta có PT: 19x² - 9x - 10 = 0
<=> (10x + 19)(x - 1) = 0
<=> x = 1 (Vì x nguyên)
KL: x = 1
\(\left(\frac{1}{24.25}+\frac{1}{25.26}+....+\frac{1}{29.30}\right).120+x=\frac{1}{3}\)
\(\left(\frac{1}{24}-\frac{1}{30}\right).120+x=\frac{1}{3}\)
120.\(\frac{1}{120}\)+x =\(\frac{1}{3}\)
1+x=\(\frac{1}{3}\)
\(\Rightarrow x=-\frac{2}{3}\)
\(\left(\frac{1}{24.25}+\frac{1}{25.26}+...+\frac{1}{29.30}\right).120+x=\frac{1}{3}\)
\(\Rightarrow\left(\frac{1}{24}-\frac{1}{25}+\frac{1}{25}+\frac{1}{26}+...+\frac{1}{29}-\frac{1}{30}\right).120+x=\frac{1}{3}\)
\(\Rightarrow\left(\frac{1}{24}-\frac{1}{30}\right).120+x=\frac{1}{3}\)
\(\Rightarrow\frac{1}{120}.120+x=\frac{1}{3}\)
\(\Rightarrow1+x=\frac{1}{3}\)
\(\Rightarrow x=\frac{1}{3}-1\)
\(\Rightarrow x=-\frac{2}{3}\)
Vậy \(x=-\frac{2}{3}.\)
Chúc bạn học tốt!