(x+1)^2-30=6
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Học sinh nhẩm và ghi kết quả như sau:
6 x 4 = 24
6 x 2 = 12
6 x 5 = 30
6 x 1 = 6
24 : 6 = 4
12 : 6 = 2
30 : 6 = 5
6 : 6 = 1
24 : 4 = 6
12 : 2 = 6
30 : 5 = 6
6 : 1 = 6
(có thể nêu nhận xét: lấy tích chia cho một thừa số được thừa số kia)
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a.
\(x\left(x-1\right)\left(x+1\right)\left(x+2\right)=24\)
\(\Leftrightarrow x\left(x+1\right).\left(x-1\right)\left(x+2\right)-24=0\)
\(\Leftrightarrow\left(x^2+x\right)\left(x^2+x-2\right)-24=0\)
Đặt \(a=x^2+x-1\) , ta có pt:
\(\left(a+1\right)\left(a-1\right)-24=0\)
\(\Leftrightarrow a^2-1-24=0\)
\(\Leftrightarrow a^2-25=0\)
\(\Leftrightarrow\left(a-5\right)\left(a+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=5\\a=-5\end{matrix}\right.\)
*Với a = 5 ta được:
\(x^2+x-1=5\)
\(\Leftrightarrow x^2+x-6=0\)
\(\Leftrightarrow x^2+3x-2x-6=0\)
\(\Leftrightarrow\left(x^2+3x\right)-\left(2x+6\right)=0\)
\(\Leftrightarrow x\left(x+3\right)-2\left(x+3\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=2\end{matrix}\right.\)
*Với a = -5 ta được:
\(x^2+x-1=-5\)
\(\Leftrightarrow x^2+x+4=0\)
\(\Leftrightarrow x^2+2.x.\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{15}{4}=0\)
\(\Leftrightarrow\left(x+\dfrac{1}{2}\right)^2+\dfrac{15}{4}=0\) ( loại)
Vậy pt có tập nghiệm là: \(s=\left\{-3;2\right\}\)
c)(ĐKXĐ: x khác 30;29)
\(\Leftrightarrow\dfrac{x-29}{30}-1+\dfrac{x-30}{29}-1=\dfrac{29}{x-30}-1+\dfrac{30}{x-29}-1\)
\(\Leftrightarrow\dfrac{x-59}{30}+\dfrac{x-59}{29}=\dfrac{x-59}{30-x}+\dfrac{x-59}{29-x}\)
\(\Leftrightarrow x=59\)(tm) or \(\dfrac{1}{30}+\dfrac{1}{29}-\dfrac{1}{30-x}-\dfrac{1}{29-x}=0\)
\(\Leftrightarrow\dfrac{-x}{30\left(30-x\right)}+\dfrac{-x}{29\left(29-x\right)}=0\)
\(\Leftrightarrow x=0\)(tm) or \(\dfrac{1}{30\left(30-x\right)}+\dfrac{1}{29\left(29-x\right)}=0\)
\(\Leftrightarrow1741-59x=0\)
\(\Leftrightarrow x=\dfrac{1741}{59}\left(tm\right)\)
Vậy S={0;\(\dfrac{1741}{59}\);59}
![](https://rs.olm.vn/images/avt/0.png?1311)
mình chỉ biết câu 1 chứ mình không biết câu 2
đáp án của mình là 2 ,mà mình không chắc cho lắm
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a) \(3\times\left(-2\right)+4\times6-2^2+\left(-2\right)^2\)
\(=\left(-6\right)+24-4+4\)
\(=18-4+4\)
\(=14+4\)
\(=18\)
b) \(-25-40+3\times6\)
\(=-25-40+18\)
\(=-65+18\)
\(=-47\)
c) \(30\times\left(-10\right)-30\times90\)
\(=\left(-300\right)-2700\)
\(=-3000\)
Chúc bạn học tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{x}{30}+\dfrac{1}{2}+\dfrac{x}{40}=5+\dfrac{1}{6}\)
\(\Leftrightarrow\dfrac{x}{30}+\dfrac{x}{40}=\dfrac{14}{3}\)
\(\Leftrightarrow\dfrac{4x+3x}{120}=\dfrac{560}{120}\)
\(\Leftrightarrow7x=560\)
\(\Leftrightarrow x=80\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, Ta có :\(-30+\left(25-x\right)=-1\)
\(\Leftrightarrow\left(-30\right)+25-x=-1\)
\(\Leftrightarrow25-x=\left(-1\right)-\left(-30\right)\)
\(\Leftrightarrow25-x=29\\ \Leftrightarrow x=25-29\)
\(\Leftrightarrow x=\left(-4\right)\)
Vậy \(x=-4\)
b,Ta có :\(\left(x+5\right)+\left(x-9\right)=x+2\)
\(\Leftrightarrow x+5+x-9=x+2\)
\(\Leftrightarrow2.x+\left(5-9\right)=x+2\)
\(\Leftrightarrow\) \(2.x+\left(-4\right)=x+2\)
\(\Leftrightarrow2.x-x=4+2\)
\(\Leftrightarrow x=6\)
Vậy \(x=6\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: =>2x-x=-5/2-1/3
=>x=-17/6
b: =>4(x-2)2=36
=>(x-2)2=9
=>x-2=3 hoặc x-2=-3
hay x=5 hoặc x=-1
c: =>2x+1/2=5/6
=>2x=1/3
hay x=1/6
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1,=\left(x+3\right)\left(x-2\right):\left(x+3\right)=x-2\\ 2,=\left(x-5\right)\left(x+6\right):\left(x+6\right)=x-5\\ 3,=\left[3x\left(2x-1\right)-5\right]:\left(2x-1\right)=3x.dư.\left(-5\right)\)
1)\(\left(x+x^2-6\right):\left(x+3\right)=\left[x\left(x+3\right)-2\left(x+3\right)\right]:\left(x+3\right)=\left[\left(x+3\right)\left(x-2\right)\right]:\left(x+3\right)=x-2\)
2) \(\left(x+x^2-30\right):\left(x+6\right)=\left[x\left(x+6\right)-5\left(x+6\right)\right]:\left(x+6\right)=\left[\left(x+6\right)\left(x-5\right)\right]:\left(x+6\right)=x-5\)
3) \(\left(5-3x+6x^2\right):\left(2x-1\right)=\left[3x\left(2x-1\right)+5\right]:\left(2x-1\right)=3x+\dfrac{5}{2x-1}\)
(x+1)2-30= 6
(x+1)2=30+6
(x+1)2= 36
(x+1)2=62
\(\Rightarrow\)x+1= 6
\(\Rightarrow\)x= 6-1
\(\Rightarrow\)x= 5
Vậy x=5
Chúc bn học tốt
#miu
#armybts
thank nhá