Cảm ơn mn trc nka:3
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\(\dfrac{x+5}{2017}+\dfrac{x+4}{2018}+\dfrac{x+3}{2019}=-3\\ \dfrac{x+5}{2017}+1+\dfrac{x+4}{2018}+1+\dfrac{x+3}{2019}=-3+3\\ \dfrac{x+5}{2017}+\dfrac{2017}{2017}+\dfrac{x+4}{2018}+\dfrac{2018}{2018}+\dfrac{x+3}{2019}+\dfrac{2019}{2019}=0\\ \dfrac{x+2022}{2017}+\dfrac{x+2022}{2018}+\dfrac{x+2022}{2019}=0\\ x+2022.\left(\dfrac{1}{2017}+\dfrac{1}{2018}+\dfrac{1}{2019}\right)=0\)
⇒x+2022=0 (vì \(\dfrac{1}{2017}+\dfrac{1}{2018}+\dfrac{1}{2019}\)\(\ne0\))
⇒x=0-2022
⇒x=-2022
Đặt t = x + 3
=> x + 2 = t - 1; x + 4 = t + 1.
ta có pt: (t - 1)^4 + (t + 1)^4 = 82
<=>[(t -1)²]² + [(t + 1)²]² = 82
<=> (t² - 2t + 1)² + (t² + 2t + 1)² = 82
<=> (t²+1)² - 4t(t²+1) + 4t² + (t²+1)² + 4t(t²+1) + 4t² = 82
<=> (t² + 1)² + 4t² = 41
<=> t^4 + 6t² + 1 = 41
<=> (t²)² + 6t² - 40 = 0
<=> t² = -10 (loại) hoặc t² = 4
<=> t = 2 hoặc t = -2
với t = -2 => x = -5
với t = 2 => x = -1
vậy pt có hai nghiệm là : x = -1 hoặc x = -5
Do \(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{b}{a}=\dfrac{d}{c}\)
\(\Rightarrow1-\dfrac{b}{a}=1-\dfrac{d}{c}\Rightarrow\dfrac{a-b}{a}=\dfrac{c-d}{c}\) (đpcm)
6,54 x 5,8 = \(\dfrac{9483}{250}\) = 37,932
220,32 : 6,8 = \(\dfrac{162}{5}\) = 32,4
\(a.720:\left(x-17\right)=12\)
\(x-17=60\)
\(x=77\)
\(b.\left(x-28\right):12=8\)
\(x-28=96\)
\(x=124\)
\(c.26+8x=6x+46\)
\(8x-6x=46-26\)
\(2x=20\)
\(x=10\)
\(d.3600:\left[\left(5x+335\right):x\right]=50\)
\(\left(5x+335\right):x=72\)
\(5+335:x=72\)
\(335:x=67\)
\(x=5\)
a) \(720:\left(x-17\right)=12\)
\(\Rightarrow x-17=\dfrac{720}{12}\)
\(\Rightarrow x-17=60\)
\(\Rightarrow x=60+17\)
\(\Rightarrow x=77\)
b) \(\left(x+28\right):12=8\)
\(\Rightarrow x+28=12\cdot8\)
\(\Rightarrow x+28=96\)
\(\Rightarrow x=96-28\)
\(\Rightarrow x=68\)
c) \(26+8x=6x+46\)
\(\Rightarrow8x-6x=46-26\)
\(\Rightarrow2x=20\)
\(\Rightarrow x=\dfrac{20}{2}\)
\(\Rightarrow x=10\)
d) \(3600:\left[\left(5x+335\right):x\right]=50\)
\(\Rightarrow\left(5x+335\right):x=\dfrac{3600}{50}\)
\(\Rightarrow\left(5x+335\right):x=72\)
\(\Rightarrow5x+335=72\cdot x\)
\(\Rightarrow72x-5x=335\)
\(\Rightarrow67x=335\)
\(\Rightarrow x=\dfrac{335}{67}\)
\(\Rightarrow x=5\)
1: \(x^2-\left(m+1\right)x-2023=0\)
a=1; b=-(m+1); c=-2023
Vì \(a\cdot c=-2023< 0\)
nên phương trình luôn có hai nghiệm phân biệt
Theo Vi-et, ta có:
\(\left\{{}\begin{matrix}x_1+x_2=-\dfrac{b}{a}=\dfrac{-\left[-\left(m+1\right)\right]}{1}=m+1\\x_2\cdot x_1=\dfrac{c}{a}=-\dfrac{2023}{1}=-2023\end{matrix}\right.\)
\(\dfrac{1}{x_1-2023}+\dfrac{1}{x_2-2023}=1\)
=>\(\dfrac{x_2-2023+x_1-2023}{\left(x_1-2023\right)\left(x_2-2023\right)}=1\)
=>\(x_2+x_1-4046=\left(x_1-2023\right)\left(x_2-2023\right)\)
=>\(m+1-4046=x_1x_2-2023\left(x_1+x_2\right)+2023^2\)
=>\(m-4045=-2023-2023\left(m+1\right)+2023^2\)
=>\(m-4045=-2023-2023m-2023+2023^2\)
=>\(2024m=4092528\)
=>\(m=\dfrac{4092528}{2024}=2022\)
15 . C
16 . A
17 . D
18 . A
19 . B