giúp mình với hứa sẽ vote 5 sao
giải các phương trình
a) 10x-5=x(2x-1)
b) __x-5__ + __x-3__ = __x-25__
x x+5 x ²+5x
c) __x-1__ – __2x__ = __7-6x__
x+3 x-3 x ²-9
giúp mình với hứa sẽ vote 5 sao
giải các phương trình
a) 10x-5=x(2x-1)
b) __x-5__ + __x-3__ = __x-25__
x x+5 x ²+5x
c) __x-1__ – __2x__ = __7-6x__
x+3 x-3 x ²-9
`a)10x-5=x(2x-1)`
`⇔5(2x-1)-x(2x-1)=0`
`⇔(2x-1)(5-x)=0`
⇔\(\left[ \begin{array}{l}2x=1\\x=5\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=\frac{1}{2}\\x=5\end{array} \right.\)
`b)x-5/x+x-3/x+5=x-25/x^2+5x` ĐK:x$\neq$ ,±5
`⇔(x-5)(x+5)/x(x+5)+x(x+3)/x(x+5)=x-25/x(x+5)`
`⇔x^2-5x+5x-25+x^2+3x-x=-25`
`⇔2x^2-4x=25-25`
`⇔2x(x-2)=0
`2x=0 hoặc x=2`
`x=0(KTM)`
`x=2(TM)`
Vậy phương trình vô nghiệm S={2}
`c)x-1/x+3-2x/x-3=7-6x/x^2-9` ĐK:x$\neq$ ±3
`⇔(x-1)(x-3)/x^2-9-2x(x+3)/x^2-9=7-6x/x^2-9`
`⇔x^2-x-3x+3-2x^2-6x=7-6x`
`⇔x^2-4x+3-7=0`
`⇔x^2-4x-4=0`
`⇔-(x+2)^2=0`
`⇔x=-2(TM)`
Xin hay nhất ạ.
Đáp án:
\(a)\,\)`S={1/2;5}`
\(b)\,\)`S={2}`
\(c)\,\)`S={-2}`
Giải thích các bước giải:
\(a)\,10x-5=x(2x-1)\\\Leftrightarrow 5(2x-1)-x(2x-1)=0\\\Leftrightarrow (2x-1)(5-x)=0\\\Leftrightarrow \left[ \begin{array}{l}2x-1=0\\5-x=0\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}2x=1\\-x=-5\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=\dfrac{1}{2}\\x=5\end{array} \right.\\b)\,\dfrac{x-5}{x}+\dfrac{x-3}{x+5}=\dfrac{x-25}{x^2+5x}\) ĐKXĐ: \(\begin{cases}x\neq0\\x\neq-5\\\end{cases}\)\(\\\Leftrightarrow \,\dfrac{(x-5)(x+5)+x(x-3)}{x(x+5)}=\dfrac{x-25}{x(x+5)}\\\Rightarrow(x-5)(x+5)+x(x-3)=x-25\\\Leftrightarrow x^2-25+x^2-3x-x+25=0\\\Leftrightarrow 2x^2-4x=0\\\Leftrightarrow 2x(x-2)=0\\\Leftrightarrow \left[ \begin{array}{l}2x=0\\x-2=0\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=0\,(ktmđk)\\x=2\,(tmđk)\end{array} \right.\\c)\,\dfrac{x-1}{x+3}-\dfrac{2x}{x-3}=\dfrac{7-6x}{x^2-9}\) ĐKXĐ: \(\begin{cases}x\neq3\\x\neq-3\\\end{cases}\) \(\\\Leftrightarrow \dfrac{(x-1)(x-3)-2x(x+3)}{(x+3)(x-3)}=\dfrac{7-6x}{(x+3)(x-3)}\\\Rightarrow (x-1)(x-3)-2x(x+3)=7-6x\\\Leftrightarrow x^2-4x+3-2x^2-6x-7+6x=0\\\Leftrightarrow -x^2-4x-4=0\\\Leftrightarrow -(x+2)^2=0\\\Leftrightarrow x=-2\,(tmđk)\)