Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Bạn cần viết đề bằng công thức toán (biểu tượng $\sum$ góc trái khung soạn thảo) đẻ được hỗ trợ tốt hơn. Viết như thế kia rất khó đọc => khả năng bị bỏ qua bài cao.
a: =>3x=3
=>x=1
b: =>12x-2(5x-1)=3(8-3x)
=>12x-10x+2=24-9x
=>2x+2=24-9x
=>11x=22
=>x=2
c: =>2x-3(2x+1)=x-6x
=>-5x=2x-6x-3=-4x-3
=>-x=-3
=>x=3
d: =>2x-5=0 hoặc x+3=0
=>x=5/2 hoặc x=-3
e: =>x+2=0
=>x=-2
\(x-5=\frac{1}{3\left(x+2\right)}\left(đkxđ:x\ne-2\right)\)
\(< =>3\left(x-5\right)\left(x+2\right)=1\)
\(< =>3\left(x^2-3x-10\right)=1\)
\(< =>x^2-3x-10=\frac{1}{3}\)
\(< =>x^2-3x-\frac{31}{3}=0\)
giải pt bậc 2 dễ r
\(\frac{x}{3}+\frac{x}{4}=\frac{x}{5}-\frac{x}{6}\)
\(< =>\frac{4x+3x}{12}=\frac{6x-5x}{30}\)
\(< =>\frac{7x}{12}=\frac{x}{30}< =>12x=210x\)
\(< =>x\left(210-12\right)=0< =>x=0\)
1. Ta có \(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16=0\)
\(\Rightarrow\)\(\left[\left(x+2\right)\left(x+8\right)\right].\left[\left(x+4\right)\left(x+6\right)\right]+16=0\)
\(\Rightarrow\left(x^2+10x+16\right)\left(x^2+10x+24\right)+16=0\)
Đặt \(x^2+10x=t\)
Pt \(\Leftrightarrow\left(t+16\right)\left(t+24\right)+16=0\Leftrightarrow t^2+40t+400=0\Leftrightarrow t=-20\)
\(\Rightarrow x^2+10x+20=0\Rightarrow\orbr{\begin{cases}x=-5+\sqrt{5}\\x=-5-\sqrt{5}\end{cases}}\)
2. Ta có \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=0\)
\(\Rightarrow\left[\left(x+2\right)\left(x+5\right)\right].\left[\left(x+3\right)\left(x+4\right)\right]-24=0\)\(\Rightarrow\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24=0\)
Đặt \(x^2+7x=t\Rightarrow\left(t+10\right)\left(t+12\right)-24=0\Rightarrow t^2+22t+96=0\)\(\Rightarrow\orbr{\begin{cases}t=-6\\t=-16\end{cases}}\)
Với \(t=-6\Rightarrow x^2+7x+6=0\Rightarrow\orbr{\begin{cases}x=-6\\x=-1\end{cases}}\)
Với \(t=-16\Rightarrow x^2+7x+16=0\left(l\right)\)
Vậy pt có 2 nghiệm là \(\orbr{\begin{cases}x=-6\\x=-1\end{cases}}\)
Quản lí Hoàng Thị Lan Hương giúp em giải bài toán vừa đăng lên đc ko ạ.??? ^^
\(a,\left(x-6\right)\left(2x-5\right)\left(3x+9\right)=0\Leftrightarrow\left[{}\begin{matrix}x-6=0\Leftrightarrow x=6\\2x-5=0\Leftrightarrow x=\dfrac{5}{2}\\3x+9=0\Leftrightarrow x=-3\end{matrix}\right.\)
\(b,2x\left(x-3\right)+5\left(x-3\right)=0\Leftrightarrow\left(2x+5\right)\left(x-3\right)=0\Leftrightarrow\left[{}\begin{matrix}x-3=0\Leftrightarrow x=3\\2x+5=0\Leftrightarrow x=-\dfrac{5}{2}\end{matrix}\right.\)
\(c,x^2-4-\left(x-2\right)\left(3-2x\right)=0\Leftrightarrow\left(x-2\right)\left(x+2\right)-\left(x-2\right)\left(3-2x\right)=0\Leftrightarrow\left(x-2\right)\left(x+2-3+2x\right)=0\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{1}{3}\end{matrix}\right.\)
\(x=-7\left(2m-5\right)x-2m^2+8\Leftrightarrow x+7\left(2m-5\right)=8-2m^2\Leftrightarrow x\left(14m-34\right)=8-2m^2\)
\(ycđb\Leftrightarrow14m-34\ne0\Leftrightarrow m\ne\dfrac{34}{14}\)\(\Rightarrow x=\dfrac{8-2m^2}{14m-34}\)
\(3.17\Leftrightarrow4x^2-4x+1-2x-1=0\Leftrightarrow4x^2-6x=0\Leftrightarrow x\left(4x-6\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{3}{2}\end{matrix}\right.\)
3.15:
a, \(\Leftrightarrow\left\{{}\begin{matrix}x-6=0\\2x-5=0\\3x+9=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=6\\x=\dfrac{5}{2}\\x=-\dfrac{9}{3}=-3\end{matrix}\right.\)
b, \(\Leftrightarrow\left(x-3\right)\left(2x+5\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-3=0\\2x+5=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\x=-\dfrac{5}{2}\end{matrix}\right.\)
c, \(\Leftrightarrow\left(x-2\right)\left(x+2\right)-\left(x-2\right)\left(3-2x\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+2-3+2x\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-2=0\\3x-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\x=\dfrac{1}{3}\end{matrix}\right.\)
3.16
\(\Leftrightarrow\left(2m-5\right).-7-2m^2+8=0\)
\(\Leftrightarrow-14m+35-2m^2+8=0\)
\(\Leftrightarrow-14m-2m^2+43=0\)
\(\Leftrightarrow-2\left(7m+m^2\right)=-43\)
\(\Leftrightarrow m\left(7-m\right)=\dfrac{43}{2}\)
\(\Leftrightarrow\dfrac{m\left(7-m\right)}{1}-\dfrac{43}{2}=0\)
\(\Leftrightarrow\dfrac{14m-2m^2}{2}-\dfrac{43}{2}=0\)
pt vô nghiệm
Mình khuyên bạn thế này :
Bạn nên tách những câu hỏi ra
Như vậy các bạn sẽ dễ giúp
Và cũng có nhiều bạn giúp hơn !
Bài 1.
a) ( x - 3 )( x + 7 ) = 0
<=> x - 3 = 0 hoặc x + 7 = 0
<=> x = 3 hoặc x = -7
Vậy S = { 3 ; -7 }
b) ( x - 2 )2 + ( x - 2 )( x - 3 ) = 0
<=> ( x - 2 )( x - 2 + x - 3 ) = 0
<=> ( x - 2 )( 2x - 5 ) = 0
<=> x - 2 = 0 hoặc 2x - 5 = 0
<=> x = 2 hoặc x = 5/2
Vậy S = { 2 ; 5/2 }
c) x2 - 5x + 6 = 0
<=> x2 - 2x - 3x + 6 = 0
<=> x( x - 2 ) - 3( x - 2 ) = 0
<=> ( x - 2 )( x - 3 ) = 0
<=> x - 2 = 0 hoặc x - 3 = 0
<=> x = 2 hoặc x = 3
cho tam giác MNP trên MN lấy điểm Y sao cho MY bằng 1/2 YN trên PY lấy điểm K sao cho YK bằng KPx2 trên PM lấy điểm E sao cho PE bằng 1/3 EM tính diện tích tam giác YKE biết diện tích tam giác MNP bằng 72 cm2
a: 11x+4=-3/2
=>\(11x=-\dfrac{3}{2}-4=-\dfrac{11}{2}\)
=>\(x=-\dfrac{1}{2}\)
b: \(x^2-9+2\left(x-3\right)=0\)
=>\(\left(x-3\right)\left(x+3\right)+2\left(x-3\right)=0\)
=>\(\left(x-3\right)\left(x+3+2\right)=0\)
=>(x-3)(x+5)=0
=>\(\left[{}\begin{matrix}x-3=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-5\end{matrix}\right.\)
c: \(\dfrac{x-3}{5}+\dfrac{1+2x}{3}=6\)
=>\(\dfrac{3\left(x-3\right)+5\left(2x+1\right)}{15}=6\)
=>\(3x-9+10x+5=90\)
=>13x-4=90
=>13x=94
=>\(x=\dfrac{94}{13}\)
d: \(\dfrac{2}{x+1}-\dfrac{1}{x-2}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\)(ĐKXĐ: \(x\notin\left\{-1;2\right\}\))
=>\(\dfrac{2\left(x-2\right)-\left(x+1\right)}{\left(x+1\right)\left(x-2\right)}=\dfrac{3x-11}{\left(x-2\right)\left(x+1\right)}\)
=>3x-11=2x-4-x-1
=>3x-11=x-5
=>2x=6
=>x=3(nhận)
\(a,\dfrac{x-3}{x}=\dfrac{x-3}{x+3}\)\(\left(đk:x\ne0,-3\right)\)
\(\Leftrightarrow\dfrac{x-3}{x}-\dfrac{x-3}{x+3}=0\)
\(\Leftrightarrow\dfrac{\left(x-3\right)\left(x+3\right)-x\left(x-3\right)}{x\left(x+3\right)}=0\)
\(\Leftrightarrow x^2-9-x^2+3x=0\)
\(\Leftrightarrow3x-9=0\)
\(\Leftrightarrow3x=9\)
\(\Leftrightarrow x=3\left(n\right)\)
Vậy \(S=\left\{3\right\}\)
\(b,\dfrac{4x-3}{4}>\dfrac{3x-5}{3}-\dfrac{2x-7}{12}\)
\(\Leftrightarrow\dfrac{4x-3}{4}-\dfrac{3x-5}{3}+\dfrac{2x-7}{12}>0\)
\(\Leftrightarrow\dfrac{3\left(4x-3\right)-4\left(3x-5\right)+2x-7}{12}>0\)
\(\Leftrightarrow12x-9-12x+20+2x-7>0\)
\(\Leftrightarrow2x+4>0\)
\(\Leftrightarrow2x>-4\)
\(\Leftrightarrow x>-2\)
`a,(2x-5)(12+5x)=0`
\(\Leftrightarrow\left[{}\begin{matrix}2x-5=0\\12+5x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=5\\5x=-12\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-\dfrac{12}{5}\end{matrix}\right.\)
`b, (x-3)(x-4)-2(x-3)=0`
`<=>(x-3)(x-4-2)=0`
`<=>(x-3)(x-6)=0`
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x-6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=6\end{matrix}\right.\)
`c, x(x-1)(x+1)=0`
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-1=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-1\end{matrix}\right.\)
`d, (2x)/3 +(2x-1)/6=0`
`<=> (4x)/6 +(2x-1)/6=0`
`<=> (4x+2x-1)/6=0`
`<=> (6x-1)/6=0`
`<=> 6x-1=0`
`<=> 6x=1`
`<=>x=1/6` ( đề là vậy à bạn )
a) \(\left(2x-5\right)\left(12+5x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-5=0\\12+5x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=5\\5x=-12\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2,5\\x=-2,4\end{matrix}\right.\)
b) \(\left(x-3\right)\left(x-4\right)-2\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left[\left(x-4\right)-2\right]=0\)
\(\Leftrightarrow\left(x-3\right)\left(x-6\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x-6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=6\end{matrix}\right.\)
c) \(x\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-1=0\\x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=1\\x=0\end{matrix}\right.\)
d) \(\dfrac{2x}{3}+\dfrac{2x-1}{6}=0\)
\(\Leftrightarrow\dfrac{4x+2x-1}{6}=0\)
\(\Leftrightarrow6x-1=0\)
\(\Leftrightarrow6x=1\Leftrightarrow x=\dfrac{1}{6}\)