Giải phương trình
x-27/1991 + x-60/1958 + x/1009 = 4
giải phương trình
x+1/2021 +x+2/2020=x+3/2019+x+4/2018
\(\dfrac{x+1}{2021}+\dfrac{x+2}{2020}=\dfrac{x+3}{2019}+\dfrac{x+4}{2018}\)
=>\(\dfrac{x+1}{2021}+1+\dfrac{x+2}{2020}+1=\dfrac{x+3}{2019}+1+\dfrac{x+4}{2018}+1\)
=>\(\dfrac{x+2022}{2021}+\dfrac{x+2022}{2020}=\dfrac{x+2022}{2019}+\dfrac{x+2022}{2018}\)
=> (x+2022)(\(\dfrac{1}{2021}+\dfrac{1}{2020}-\dfrac{1}{2019}-\dfrac{1}{2018}\))=0
=>x+2022=0
=> x=-2022
giải phương trình
x-4\(\sqrt{x-2}\)+1=0
\(x-4\sqrt{x-2}+1=0\)(Đk x>2)
⇔\(x-2-4\sqrt{x-2}+4-1=0\)
\(\Leftrightarrow\left(\sqrt{x-2}-2\right)^2-1=0\)
\(\Leftrightarrow\left(\sqrt{x-2}-3\right)\left(\sqrt{x-2}-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-2}-3=0\\\sqrt{x-2}-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-2}=3\\\sqrt{x-2}=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=9\\x-2=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=11\\x=3\end{matrix}\right.\)(thảo đk)
Vậy\(\left[{}\begin{matrix}x=11\\x=3\end{matrix}\right.\)là nghiệm của pt
ĐKXĐ: x≥2
x+1=\(4\sqrt{x-2}\) bình phương 2 vế ta đc:\(\left(x+1\right)^2=16\cdot\left(x-2\right)< =>x^2+2x+1=16x-32< =>x^2-14x+33=0\)
giải phương trình này ta đc:x1=11(nhận); x2=3(nhận)
vậy phương trình có 2 nghiệm: x1=11;x2=3
Giải phương trình
X +\(\sqrt{9-X^2}-X\sqrt[]{9-X^2}\)=3
\(x+\sqrt{9-x^2}-x\sqrt{9-x^2}=3\left(-3\le x\le3\right)\)
\(\Leftrightarrow\sqrt{9-x^2}-x\sqrt{9-x^2}=3-x\\ \Leftrightarrow9-x^2+x^2\left(9-x^2\right)-2x\sqrt{\left(9-x^2\right)^2}=9-6x+x^2\\ \Leftrightarrow9+8x^2-x^4-2x\left(9-x^2\right)=x^2-6x+9\\ \Leftrightarrow-x^4+2x^3+7x^2-12x=0\\ \Leftrightarrow-x\left(x^3-2x^2-7x+12\right)=0\Leftrightarrow-x\left(x^3-3x^2+x^2-3x-4x+12\right)=0\\ \Leftrightarrow x\left(x-3\right)\left(x^2+x-4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\left(N\right)\\x=3\left(N\right)\\x^2+x-4=0\left(1\right)\end{matrix}\right.\)
\(\Delta\left(1\right)=1-4\left(-4\right)=17>0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-1-\sqrt{17}}{2}\left(N\right)\\x=\dfrac{-1+\sqrt{17}}{2}\left(N\right)\end{matrix}\right.\)
Vậy \(S=\left\{0;3;\dfrac{-1-\sqrt{17}}{2};\dfrac{-1+\sqrt{17}}{2}\right\}\)
Tick ✔
Giải bất phương trình
x-1/x-3>1 (đk: x#3)
giải giúp mình với ạ
\(\dfrac{x-1}{x-3}>1\left(x\ne3\right)\)
\(\Leftrightarrow\dfrac{x-1-x+3}{x-3}>0\)
\(\Leftrightarrow2>0\)
Vậy \(S=\left\{2\right\}\)
-ĐKXĐ: \(x\ne3\)
\(\dfrac{x-1}{x-3}>1\)
\(\Leftrightarrow\dfrac{x-1}{x-3}-\dfrac{x-3}{x-3}>0\)
\(\Leftrightarrow\dfrac{x-1-x+3}{x-3}>0\)
\(\Leftrightarrow\dfrac{2}{x-3}>0\)
\(\Leftrightarrow x-3>0\)
\(\Leftrightarrow x>3\)
-Vậy tập nghiệm của BĐT là {x l x>3}
Giải phương trình
X-15/7 + x-36/16 + x-58/14 + x-76/12 = 14
Sửa đề: (x-15)/17
=>\(\left(\dfrac{x-15}{17}-5\right)+\left(\dfrac{x-36}{16}-4\right)+\left(\dfrac{x-58}{14}-3\right)+\left(\dfrac{x-76}{12}-2\right)=0\)=>x-100=0
=>x=100
Giải hệ phương trình
x - 1/y = 1
y - 1/z = 1
z - 1/x = 1
Giải hệ phương trình
x(y+z)=-1
y(x+z)=-9
z(x+y)=-4
Làm giúp em ạ em cảm ơn
giải phương trình x-2/2016 +x-4/1009+x-6/2020=-4
\(\dfrac{x-2}{2016}+\dfrac{x-4}{1009}+\dfrac{x-6}{2020}=-4\)
\(\Leftrightarrow\) \(\dfrac{x-2}{2016}+1+\dfrac{x-4}{1009}+2+\dfrac{x-6}{2020}+1=0\)
\(\Leftrightarrow\) \(\dfrac{x-2+2016}{2016}+\dfrac{x-4+2018}{1009}+\dfrac{x-6+2020}{2020}=0\)
\(\Leftrightarrow\) \(\dfrac{x-2014}{2016}+\dfrac{x-2014}{1009}+\dfrac{x-2014}{2020}=0\)
\(\Leftrightarrow\) \(\left(x-2014\right)\left(\dfrac{1}{2016}+\dfrac{1}{1009}+\dfrac{1}{2020}\right)=0\)
\(\Leftrightarrow\) x - 2014 = 0
\(\Leftrightarrow\) x = 2014
Vậy............