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aGiải phương trình |x-1|+|x-2|=|2x-3|
b)Giải phương trình 1/(x−2 )+ 2/(x−3) − 3/(x−5) = 1/(x^2 −5x+6)
1. a = 3 thì phương trình trở thành:
\(\frac{x+3}{3-x}-\frac{x-3}{3+x}=\frac{-3\left[3.\left(-3\right)+1\right]}{\left(-3\right)^2}-x^2\)
\(\Leftrightarrow\frac{\left(x+3\right)^2+\left(3-x\right)^2}{\left(3-x\right)\left(3+x\right)}=\frac{-3\left[-9+1\right]}{9}-x^2\)
\(\Leftrightarrow\frac{x^2+6x+9+x^2-6x+9}{\left(3-x\right)\left(3+x\right)}=\frac{-3.\left(-8\right)}{9}-x^2\)
\(\Leftrightarrow\frac{2x^2+18}{9-x^2}=\frac{24}{9}-x^2\)
\(\Leftrightarrow\frac{2x^2+18}{9-x^2}+x^2=\frac{24}{9}\)
\(\Leftrightarrow\frac{2x^2+18+9x^2-x^4}{9-x^2}=\frac{24}{9}\)
\(\Leftrightarrow\frac{11x^2+18-x^4}{9-x^2}=\frac{24}{9}\)
\(\Leftrightarrow99x^2+18-9x^4=216-24x^2\)
\(\Leftrightarrow9x^4-123x^2+198=0\)
Đặt \(x^2=t\left(t\ge0\right)\)
Phương trình trở thành \(9t^2-123t+198=0\)
Ta có \(\Delta=123^2-4.9.198=8001,\sqrt{\Delta}=3\sqrt{889}\)
\(\Rightarrow\orbr{\begin{cases}t=\frac{123+3\sqrt{889}}{18}=\frac{41+\sqrt{889}}{6}\\t=\frac{123-3\sqrt{889}}{18}=\frac{41-\sqrt{889}}{6}\end{cases}}\)
Lúc đó \(\orbr{\begin{cases}x^2=\frac{41+\sqrt{889}}{6}\\x^2=\frac{41-\sqrt{889}}{6}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\pm\sqrt{\frac{41+\sqrt{889}}{6}}\\x=\pm\sqrt{\frac{41-\sqrt{889}}{6}}\end{cases}}\)
Vậy pt có 4 nghiệm \(S=\left\{\pm\sqrt{\frac{41+\sqrt{889}}{6}};\pm\sqrt{\frac{41-\sqrt{889}}{6}}\right\}\)
a: 7x+35=0
=>7x=-35
=>x=-5
b: \(\dfrac{8-x}{x-7}-8=\dfrac{1}{x-7}\)
=>8-x-8(x-7)=1
=>8-x-8x+56=1
=>-9x+64=1
=>-9x=-63
hay x=7(loại)
a, \(7x=-35\Leftrightarrow x=-5\)
b, đk : x khác 7
\(8-x-8x+56=1\Leftrightarrow-9x=-63\Leftrightarrow x=7\left(ktm\right)\)
vậy pt vô nghiệm
2, thiếu đề
=>\(\dfrac{x-2-3x+3}{\left(x-1\right)\left(x-2\right)}=\dfrac{-1}{\left(x-1\right)\left(x-2\right)}\)
=>-2x+1=-1
=>-2x=-2
=>x=1(loại)
\(\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+....+\dfrac{1}{\left(x+2020\right)\left(x+2021\right)=1}\)
\(\Leftrightarrow\dfrac{1}{x+1}-\dfrac{1}{x+2}+\dfrac{1}{x+2}-\dfrac{1}{x+3}+...+\dfrac{1}{x+2020}-\dfrac{1}{x+2021}=1\)
\(\Leftrightarrow\dfrac{1}{x+1}-\dfrac{1}{x+2021}=1\)
\(\Leftrightarrow\dfrac{\left(x+2021\right)-\left(x+1\right)}{\left(x+1\right)\left(x+2021\right)}=1\)
\(\Leftrightarrow\dfrac{x+2021-x-1}{\left(x+1\right)\left(x+2021\right)}=1\)
\(\Leftrightarrow\dfrac{2020}{\left(x+1\right)\left(x+2021\right)}=1\)
\(\Leftrightarrow\left(x+1\right)\left(x+2021\right)=2020\)
\(\Leftrightarrow x^2+2021x+x+2021=2020\)
\(\Leftrightarrow x^2+2022x=-1\)
\(\Leftrightarrow x\left(x+2022\right)=-1\)
Đến đây bạn chia trường hợp để giaỉ ra nghiệm nguyên nhé
\(\dfrac{1}{x-1}-\dfrac{2}{2-x}=\dfrac{5}{\left(x-1\right)\left(x-2\right)}\)
\(\Leftrightarrow\dfrac{1}{x-1}+\dfrac{2}{x-2}=\dfrac{5}{\left(x-1\right)\left(x-2\right)}\)
ĐKXĐ : \(\left\{{}\begin{matrix}x-1\ne0\\x-2\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne1\\x\ne2\end{matrix}\right.\)
Ta có : \(\dfrac{1}{x-1}+\dfrac{2}{x-2}=\dfrac{5}{\left(x-1\right)\left(x-2\right)}\)
\(\Leftrightarrow\dfrac{x-2}{\left(x-1\right)\left(x-2\right)}+\dfrac{2\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}=\dfrac{5}{\left(x-1\right)\left(x-2\right)}\)
`=> x-2+2(x-1)=5`
`<=> x-2+2x-2=5`
`<=> 3x-4=5`
`<=> 3x=9`
`<=>x=3` ( thỏa mãn đk )
Vậy pt đã cho có nghiệm `x=3`
` @` Đề như này nhỉ ^^
\(chucbanhoctot\)
minh biet
ta có :
\(\left|x+1\right|+\left|x-1\right|=1+\left|\left(x-1\right)\left(x+1\right)\right|\)
\(\Leftrightarrow\left|x-1\right|\left|x+1\right|-\left|x-1\right|-\left|x+1\right|+1=0\)
\(\Leftrightarrow\left(\left|x-1\right|-1\right)\left(\left|x+1\right|-1\right)=0\Leftrightarrow\orbr{\begin{cases}\left|x-1\right|=1\\\left|x+1\right|=1\end{cases}}\)
\(\Leftrightarrow x\in\left\{-2,0,2\right\}\)