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25 tháng 8 2021
e: Ta có: \(2x\left(x-5\right)-26=x\left(2x+3\right)\)
\(\Leftrightarrow2x^2-10x-26-2x^2-3x=0\)
\(\Leftrightarrow-13x=26\)
hay x=-2
f: Ta có: \(x^2-9=-2x\left(x-3\right)\)
\(\Leftrightarrow\left(x-3\right)\left(x+3\right)+2x\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(3x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)
g: Ta có: \(4x^3-9x=0\)
\(\Leftrightarrow x\left(2x-3\right)\left(2x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{3}{2}\\x=-\dfrac{3}{2}\end{matrix}\right.\)
h: Ta có: \(x^2-8x+2\left(x-8\right)=0\)
\(\Leftrightarrow\left(x-8\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-2\end{matrix}\right.\)
NT
25 tháng 8 2021
e. \(2x\left(x-5\right)-26=x\left(3+2x\right)\)
\(\Leftrightarrow2x^2-10x-26=3x+2x^2\)
\(\Leftrightarrow2x^2-10x-3x-2x^2=26\)
\(\Leftrightarrow-13x=26\) \(\Leftrightarrow x=-2\)
g. \(4x^3-9x=0\)
\(\Leftrightarrow x\left(4x^2-9\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\4x^2-9=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2=\dfrac{9}{4}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\pm\dfrac{3}{2}\end{matrix}\right.\)
i. \(x^3-5x=0\)
\(\Leftrightarrow x\left(x^2-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2-5=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2=5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\pm\sqrt{5}\end{matrix}\right.\)
k. \(x^2=10x-25\)
\(\Leftrightarrow x^2-10x+25=0\)
\(\Leftrightarrow\left(x-5\right)^2=0\)
\(\Leftrightarrow x-5=0\)
\(\Leftrightarrow x=5\)
f. \(x^2-9=-2x\left(x-3\right)\)
\(\Leftrightarrow\left(x-3\right)\left(x+3\right)=-2x\left(x-3\right)\)
\(\Leftrightarrow x+3=-2x\)
\(\Leftrightarrow3x=-3\)
\(\Leftrightarrow x=-1\)
h. \(x^2-8x+2\left(x-8\right)=0\)
\(\Leftrightarrow x\left(x-8\right)+2\left(x-8\right)=0\)
\(\Leftrightarrow\left(x-8\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-8=0\\x+2=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-2\end{matrix}\right.\)
j. \(x\left(x-5\right)-x+5=0\)
\(\Leftrightarrow x\left(x-5\right)-\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x-1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=1\end{matrix}\right.\)
l. \(2x^3-72x=0\)
\(\Leftrightarrow2x\left(x^2-36\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2-36=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2=36\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\pm6\end{matrix}\right.\)
25 tháng 8 2021
Bài 2:
Ta có: \(3n^3+10n^2-5⋮3n+1\)
\(\Leftrightarrow3n^3+n^2+9n^2+3n-3n-1-4⋮3n+1\)
\(\Leftrightarrow3n+1\in\left\{1;-1;2;-2;4;-4\right\}\)
\(\Leftrightarrow3n\in\left\{0;-3;3\right\}\)
hay \(n\in\left\{0;-1;1\right\}\)
KH
8 tháng 5 2021
Hướng làm:
Thấy cả tử mẫu cộng lại đều bằng 2021 → Cộng thêm 1 rồi quy đồng với mỗi phân thức
\(\dfrac{x+2}{2019}+1+\dfrac{x+3}{2018}+1=\dfrac{x+4}{2017}+1+\dfrac{x}{2021}+1\\ \Leftrightarrow\dfrac{x+2021}{2019}+\dfrac{x+2021}{2018}-\dfrac{x+2021}{2017}-\dfrac{x+2021}{2021}=0\\ \Leftrightarrow\left(x+2021\right)\left(\dfrac{1}{2019}+\dfrac{1}{2018}-\dfrac{1}{2017}-\dfrac{1}{2021}\right)=0\\ \Leftrightarrow x+2021=0\Leftrightarrow x=-2021\)
TM
8 tháng 5 2021
\(< =>\dfrac{x+2}{2019}+1+\dfrac{x+3}{2018}+1=\dfrac{x+4}{2017}+1+\dfrac{x}{2021}+1\)
\(< =>\dfrac{x+2+2019}{2019}+\dfrac{x+3+2018}{2018}=\dfrac{x+4+2017}{2017}+\dfrac{x+2021}{2021}\)
\(< =>\dfrac{x+2021}{2019}+\dfrac{x+2021}{2018}-\dfrac{x+2021}{2017}-\dfrac{x+2021}{2021}=0\)
\(< =>\left(x+2021\right)\left(\dfrac{1}{2019}+\dfrac{1}{2018}-\dfrac{1}{2017}-\dfrac{1}{2021}=\right)=0\)
\(< =>x+2021=0< =>x=-2021\)
Vậy....
DD
Đoàn Đức Hà
Giáo viên
8 tháng 5 2021
\(\frac{x+2}{2019}+\frac{x+3}{2018}=\frac{x+4}{2017}+\frac{x}{2021}\)
\(\Leftrightarrow\frac{x+2}{2019}+1+\frac{x+3}{2018}+1=\frac{x+4}{2017}+1+\frac{x}{2021}+1\)
\(\Leftrightarrow\frac{x+2021}{2019}+\frac{x+2021}{2018}=\frac{x+2021}{2017}+\frac{x+2021}{2021}\)
\(\Leftrightarrow x+2021=0\)
\(\Leftrightarrow x=-2021\)
23 tháng 7 2021
11)11) 3x(x-5)2-(x+2)3+2(x-1)3-(2x+1)(4x2-2x+1)=3x(x2-10x+25)-(x3+6x2+12x+8)+2(x3-3x2+3x-1)-(8x3+1)=3x3-30x2+75x-x3-6x2-12x-8+2x3-6x2+6x-2-8x3-1=-4x3-42x2+63x-11
29 tháng 7 2023
2:
Gọi độ dài AB là x
Độ dài lúc về là x-5
Theo đề, ta có hệ phương trình:
\(\dfrac{x-5}{10}-\dfrac{x}{12}=\dfrac{2}{3}\)
=>1/10x-5/12-1/12x=2/3
=>1/60x=2/3+5/12=8/12+5/12=13/12
=>x=13/12*60=65
TT
Giúp e bài 2 thôi ạ bài 1 e làm r ạ! Mong mn giúp e, e cần gấp ạ!
0
8 tháng 5 2021
ĐKXĐ: \(x\notin\left\{0;-9\right\}\)
Ta có: \(\dfrac{1}{x+9}-\dfrac{1}{x}=\dfrac{1}{5}+\dfrac{1}{4}\)
\(\Leftrightarrow\dfrac{20x}{20x\left(x+9\right)}-\dfrac{20\left(x+9\right)}{20x\left(x+9\right)}=\dfrac{4x\left(x+9\right)+5x\left(x+9\right)}{20x\left(x+9\right)}\)
Suy ra: \(4x^2+36x+5x^2+45x=20x-20x-180\)
\(\Leftrightarrow9x^2+81x+180=0\)
\(\Leftrightarrow x^2+9x+20=0\)
\(\Leftrightarrow x^2+4x+5x+20=0\)
\(\Leftrightarrow x\left(x+4\right)+5\left(x+4\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\left(nhận\right)\\x=-5\left(nhận\right)\end{matrix}\right.\)
Vậy: S={-4;-5}
Bài 2:
a:\(18a^2b-54a^2b^2+72ab\)
\(=18ab\left(a-3ab+4\right)\)
b: \(7a-b^2+7b-ab\)
\(=7\left(a+b\right)-b\left(a+b\right)\)
\(=\left(a+b\right)\left(7-b\right)\)
c: \(a^2-9b^2-6a+9\)
\(=\left(a-3\right)^2-9b^2\)
\(=\left(a-3-3b\right)\left(a-3+3b\right)\)
Bài 4:
Ta có: \(X=a^3-3a^2+3a\)
\(=a^3-3a^2+3a-1+1\)
\(=\left(a-1\right)^3+1\)
\(=100^3+1=1000001\)
Bài 3:
a: Ta có: \(5a\left(5a-1\right)-\left(5a+1\right)\left(5a-1\right)=8\)
\(\Leftrightarrow25a^2-5a-25a^2+1=8\)
\(\Leftrightarrow5a=-7\)
hay \(a=-\dfrac{7}{5}\)
b: Ta có: \(a^2-3a+9-3a=0\)
\(\Leftrightarrow a\left(a-3\right)-3\left(a-3\right)=0\)
\(\Leftrightarrow\left(a-3\right)^2=0\)
\(\Leftrightarrow a-3=0\)
hay a=3