giải phương trình:
\(\dfrac{2x}{3x^2-x+2}-\dfrac{7x}{3x^2+5x+2}=1\)
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DC
2
27 tháng 2 2021
`(2x)/(3x^2-x+2)-(7x)/(3x^2+5x+2)=1(x ne -1,-2/3)`
Đặt `a=3x^2+2x+2(a>=5/3)`
`pt<=>(2x)/(a-3x)-(7x)/(a+3x)=1`
`=>2x(a+3x)-7x(a-3x)=a^2-9x^2`
`<=>2ax+6x^2-7ax+21x^2=a^2-9x^2`
`<=>-5ax+27x^2=a^2-9x^2`
`<=>a^2-36x^2+5ax=0`
`<=>a^2-4ax+9ax-36x^2=0`
`<=>a(a-4x)+9x(a-4x)=0`
`<=>(a-4x)(a+9x)=0`
`+)a=4x`
`=>3x^2+2x+2=4x`
`=>3x^2-2x+2=0`
`=>x^2-2/3x+2/3=0`
`=>(x-1/3)^2+5/9=0` vô lý
`+)a+9x=0`
`=>3x^2+2x+2+9x=0`
`=>3x^2+11x+2=0`
`=>x^2+11/3x+2/3=0`
`=>x=(-11+-\sqrt{97})/6`
27 tháng 2 2021
ĐKXĐ: \(x\ne-1;x\ne-\dfrac{2}{3}\)
Ta có: \(\dfrac{2x}{3x^2-x+2}-\dfrac{7x}{3x^2+5x+2}=1\)(1)
\(\Leftrightarrow\dfrac{2}{3x-1+\dfrac{2}{x}}-\dfrac{7}{3x+5+\dfrac{2}{x}}=1\)
Đặt: \(3x+\dfrac{2}{x}=a\) (x khác 0) thì pt(1) trở thành:
\(\dfrac{2}{a-1}-\dfrac{7}{a+5}=1\)
\(\Leftrightarrow\dfrac{2\left(a+5\right)-7\left(a-1\right)}{\left(a-1\right)\left(a+5\right)}=1\)
\(\Leftrightarrow2\left(a+5\right)-7\left(a-1\right)=\left(a-1\right)\left(a+5\right)\)
\(\Leftrightarrow-5a+17=a^2+4a-5\)
\(\Leftrightarrow a^2+4a+5-5-17=0\)
\(\Leftrightarrow a^2+9a-22=0\)
\(\Leftrightarrow\left(a-2\right)\left(a+11\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=2\\a=-11\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x+\dfrac{2}{x}=2\\3x+\dfrac{2}{x}=-11\end{matrix}\right.\)
Vì \(\left\{{}\begin{matrix}3x^2+2-2x\ne0\\3x^2+11x+2\ne0\end{matrix}\right.\)
=> PT vô nghiệm
Ủa hình như sai:vvv
NH
20 tháng 3 2023
a)
`2x-3=2-x`
`<=>2x+x=2+3`
`<=>3x=5`
`<=>x=5/3`
b)
`3x+3=7+5x`
`<=>3x-5x=7-3`
`<=>-2x=4`
`<=>x=-2`
c)
`7x-3=3x+13`
`<=>7x-3x=13+3`
`<=>4x=16`
`<=>x=4`
d)
`(5x-2)/3=(5-3x)/2`
`<=>10x-4=15-9x`
`<=>10x+9x=15+4`
`<=>19x=19`
`<=>x=1`
19 tháng 2 2022
a: \(\Leftrightarrow7\left(7-3x\right)+12\left(5x+2\right)=84\left(x+13\right)\)
\(\Leftrightarrow49-21x+60x+24=84x+1092\)
\(\Leftrightarrow39x-84x=1092-73\)
=>-45x=1019
hay x=-1019/45
b: \(\Leftrightarrow21\left(x+3\right)-14=4\left(5x+9\right)-7\left(7x-9\right)\)
=>21x+63-14=20x+36-49x+63
=>21x+49=-29x+99
=>50x=50
hay x=1
c: \(\Leftrightarrow7\left(2x+1\right)-3\left(5x+2\right)=21x+63\)
=>14x+7-15x-6-21x-63=0
=>-22x-64=0
hay x=-32/11
d: \(\Leftrightarrow35\left(2x-3\right)-15\left(2x+3\right)=21\left(4x+3\right)-17\cdot105\)
=>70x-105-30x-45=84x+63-1785
=>40x-150-84x+1722=0
=>-44x+1572=0
hay x=393/11
2
11 tháng 1 2023
Bài `1:`
`h)(3/4x-1)(5/3x+2)=0`
`=>[(3/4x-1=0),(5/3x+2=0):}=>[(x=4/3),(x=-6/5):}`
______________
Bài `2:`
`b)3x-15=2x(x-5)`
`<=>3(x-5)-2x(x-5)=0`
`<=>(x-5)(3-2x)=0<=>[(x=5),(x=3/2):}`
`d)x(x+6)-7x-42=0`
`<=>x(x+6)-7(x+6)=0`
`<=>(x+6)(x-7)=0<=>[(x=-6),(x=7):}`
`f)x^3-2x^2-(x-2)=0`
`<=>x^2(x-2)-(x-2)=0`
`<=>(x-2)(x^2-1)=0<=>[(x=2),(x^2=1<=>x=+-2):}`
`h)(3x-1)(6x+1)=(x+7)(3x-1)`
`<=>18x^2+3x-6x-1=3x^2-x+21x-7`
`<=>15x^2-23x+6=0<=>15x^2-5x-18x+6=0`
`<=>(3x-1)(5x-1)=0<=>[(x=1/3),(x=1/5):}`
`j)(2x-5)^2-(x+2)^2=0`
`<=>(2x-5-x-2)(2x-5+x+2)=0`
`<=>(x-7)(3x-3)=0<=>[(x=7),(x=1):}`
`w)x^2-x-12=0`
`<=>x^2-4x+3x-12=0`
`<=>(x-4)(x+3)=0<=>[(x=4),(x=-3):}`
2
11 tháng 1 2023
`m)(1-x)(5x+3)=(3x-7)(x-1)`
`<=>(1-x)(5x+3)+(1-x)(3x-7)=0`
`<=>(1-x)(5x+3+3x-7)=0`
`<=>(1-x)(8x-4)=0<=>[(x=1),(x=1/2):}`
`p)(2x-1)^2-4=0`
`<=>(2x-1-2)(2x-1+2)=0`
`<=>(2x-3)(2x+1)=0<=>[(x=3/2),(x=-1/2):}`
`r)(2x-1)^2=49`
`<=>(2x-1-7)(2x-1+7)=0`
`<=>(2x-8)(2x+6)=0<=>[(x=4),(x=-3):}`
`t)(5x-3)^2-(4x-7)^2=0`
`<=>(5x-3-4x+7)(5x-3+4x-7)=0`
`<=>(x+4)(9x-10)=0<=>[(x=-4),(x=10/9):}`
`u)x^2-10x+16=0`
`<=>x^2-8x-2x+16=0`
`<=>(x-2)(x-8)=0<=>[(x=2),(x=8):}`
TT
20 tháng 4 2021
PT 2
\(\Leftrightarrow\dfrac{3}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}+\dfrac{2x}{\left(x-2\right)\left(x-3\right)}-\dfrac{1}{\left(x-1\right)\left(x-2\right)}=0\) ( \(x\ne1;x\ne2;x\ne3\))
\(\Leftrightarrow\dfrac{3+2x^2-2x-x+3}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}=0\)
\(\Rightarrow2x^2-3x+6=0\)
=> PT vô nghiệm.
LA
0
1 tháng 1 2019
\(\dfrac{2x-1}{3x^2+7x+2}+\dfrac{3}{9x^2+15x+4}-\dfrac{2x+7}{3x^2-5x-12}=\dfrac{5}{x+2}\)
\(\Leftrightarrow\dfrac{2x-1}{\left(3x+1\right)\left(x+2\right)}+\dfrac{3}{\left(3x+1\right)\left(3x+4\right)}-\dfrac{2x+7}{\left(4x+3\right)\left(x-3\right)}=\dfrac{5}{x+2}\)
\(\Leftrightarrow\dfrac{1}{x+2}-\dfrac{1}{3x+1}+\dfrac{1}{3x+1}-\dfrac{1}{3x+4}+\dfrac{1}{3x+4}-\dfrac{1}{x-3}=\dfrac{5}{x+2}\)
\(\Leftrightarrow\dfrac{1}{x+2}-\dfrac{1}{x-3}=\dfrac{5}{x+2}\)
\(\Leftrightarrow\dfrac{x-3-x-2}{\left(x+2\right)\left(x-3\right)}=\dfrac{5\left(x-3\right)}{\left(x+2\right)\left(x-3\right)}\)
\(\Leftrightarrow5x-3=-5\)
\(\Leftrightarrow x=-\dfrac{2}{5}\)
Vậy...
Lời giải:
ĐKXĐ:.....
Ta có: \(\frac{2x}{3x^2-x+2}-\frac{7x}{3x^2+5x+2}=1\)
\(\Leftrightarrow \frac{1}{6}+\frac{2x}{3x^2-x+2}-7\left(\frac{x}{3x^2+5x+2}+\frac{1}{6}\right)=0\)
\(\Leftrightarrow \frac{3x^2+11x+2}{6(3x^2-x+2)}-\frac{7(3x^2+11x+2)}{6(3x^2+5x+2)}=0\)
\(\Leftrightarrow \frac{1}{6}(3x^2+11x+2)\left(\frac{1}{3x^2-x+2}-\frac{7}{3x^2+5x+2}\right)=0\)
TH1: \(3x^2+11x+2=0\)
\(\Leftrightarrow x=\frac{-11\pm \sqrt{97}}{6}\) (thỏa mãn)
TH2: \(\frac{1}{3x^2-x+2}-\frac{7}{3x^2+5x+2}=0\)
\(\Leftrightarrow \frac{2}{3x^2-x+2}-\frac{7}{3x^2+5x+2}=\frac{1}{3x^2-x+2}\)
\(\Leftrightarrow \frac{1}{x}=\frac{1}{3x^2-x+2}\)
\(\Leftrightarrow x=3x^2-x+2\)
\(\Leftrightarrow 3x^2-2x+2=0\)
\(\Leftrightarrow 2x^2+(x-1)^2+1=0\) (vô lý)
Do đó PT có nghiệm \(x=\frac{-11\pm \sqrt{97}}{6}\)
Edogawa Conan: đúng hay không bạn cứ thử giá trị của x đã tính vào là được :)