3. I'm a writer, and I work ......1....... home. It doesn't particulaly matter where my house is, as long as it is ......3....... nice house. But last year my wife ........4..... a job in a different part of the country. So, we had to move. This was our first ..........5........ of ......6....... one house and selling another at the same time. I wouldn't like to do it again. We quickly saw the house .........7........ we wanted. It was then that our problems began: The people who wanted to buy our house couldn't sell ........8......... and the man whose house we wanted couldn't find a ……. he liked. It ........10......... us nine months to buy the house. Now, I'm not sure if I like it.
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h: =>7x-21-15+5x=11x-5
=>12x-36=11x-5
hay x=31
l: (x+3)(x-4)=0
=>x+3=0 hoặc x-4=0
=>x=-3 hoặc x=4
i: =>5x-30-2x-6=12
=>3x-36=12
hay x=16
m: =>119+27x=8x52
=>27x=297
hay x=11
b) 3(x - 2) = x(x - 2)
3(x - 2) - x(x - 2) = 0
=> (x - 2)(3 - x) = 0
TH1 : x - 2 = 0
=> x = 2
TH2 : 3 - x = 0
=> x = 3
Vậy x = 2 hoặc 3
c) (x + 3)7 = 4(x + 3) . 5
=> (x + 3)7 = 20(x + 3)
=> (x + 3)7 - 20(x + 3) = 0
\(\Rightarrow\left(x+3\right)\left[\left(x+3\right)^6-20\right]=0\)
TH1 : x + 3 = 0
=> x = -3
TH2 : (x + 3)6 - 20 = 0
=> (x + 3)6 = 20 (loại)
Vậy x = -3
d) x - 3.(x - 3) = x - 3
=> x - 3x + 9 = x - 3
=> x - 3x - x = -3 - 9
=> -3x = -12
=> x = 4
Vậy x = 4
\(\dfrac{x^4+3x^3-17x^2+ax+b}{x^2+5x-3}\)
\(=\dfrac{x^4+5x^3-3x^2-2x^3-10x^2+6x-4x^2-20x+12+\left(a+14\right)x+b-12}{x^2+5x-3}\)
\(=x^2-2x-4+\dfrac{\left(a+14\right)x+b-12}{x^2+5x-3}\)
Để đây là phép chia hết cho a+14=0 và b-12=0
=>a=-14 và b=12
=>a+b=-2
mình nhớ là bạn đã đăng r.Ko có việc j làm thì cx đừng đăng lại chứ!!!!!!!!!1
a)
a) a3 + b3
= (a + b)(a2 - ab + b2)
= (a + b)(a2 + 2ab + b2 - 3ab)
= (a + b)[(a + b)2 - 3ab] = (a + b)3 - 3ab(a + b)
b)
(a - b)3 + 3ab(a - b)
= a3 - 3a2.b + 3.ab2 - b3+ 3a2b - 3ab2
= a3- b3
áp dụng
\(a^3+b^3\)
\(=\left(a+b\right)^3-3ab\left(a+b\right)\)
\(=\left(-5\right)^3-3.6.\left(-5\right)\)
\(=-125+90\)
\(=-35\)
Chứng minh rằng :
\(a.\)
\(3^{n+2}-2^{n+2}+3^n-2^n⋮10\)
\(b.\)
\(3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}⋮6\)
\(.a.\) \(3^{n+2}-2^{n+2}+3^n-2^n⋮10\)
Ta có : \(3^{n+2}-2^{n+2}+3^n-2^n\)
\(=3^n.\left(3^2+2\right)-2^n.\left(2^2+1\right)\)
\(=3^n.10-2^{n-1}.2.5\)
\(=3^n.10-2^{n-1}.10\)
\(=10.\left(3^n-2^{n-1}\right)⋮10\) \(\left(dpcm\right)\)
Vậy : \(3^{n+2}-2^{n+2}+3^n-2^n⋮10\)
\(.b.\) \(3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}⋮6\)
Ta có : \(3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}\) \(=3^n.\left(3^3+3\right)+2^n.\left(2^3+2^2\right)\)\(=3^n.30+2^n.12\)
\(=6\left(3^n.5+2^{n+1}\right)⋮6\) \(\left(dpcm\right)\)
Vậy : \(3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}⋮6\)
a)\(VT=3^{n+2}-2^{n+2}+3^n-2^n\)
\(=\left(3^{n+2}+3^n\right)-\left(2^{n+2}+2^n\right)\)
\(=3^n\left(3^2+1\right)-2^n\left(2^2+1\right)\)
\(=3^n\cdot10-2^n\cdot5\)
\(=3^n\cdot10-2^{n-1}\cdot2\cdot5\)
\(=3^n\cdot10-2^{n-1}\cdot10\)
\(=10\cdot\left(3^n-2^{n-1}\right)⋮10\)
b)\(VT=3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}\)
\(=\left(3^{n+3}+3^{n+1}\right)+\left(2^{n+3}+2^{n+2}\right)\)
\(=3^{n+1}\left(3^2+1\right)+2^{n+2}\left(2+1\right)\)
\(=3^{n+1}\cdot10+2^{n+2}\cdot3\)
\(=3^n\cdot3\cdot2\cdot5+2^{n+1}\cdot2\cdot3\)
\(=3^n\cdot5\cdot6+2^{n+1}\cdot6\)
\(=6\cdot\left(3^n\cdot5+2^{n+1}\right)⋮6\)
bài 1) a) \(1+2+3+4+........+2005+2006\)
\(\Leftrightarrow\) \(\left(1+2006\right)+\left(2+2005\right)+........+\left(1003+1004\right)\)
\(\Leftrightarrow\) \(2007.\dfrac{2006}{2}=2007.1003=2013021\)
b) \(5+10+15+.......+2000+2005\)
\(\Leftrightarrow\) \(\left(2005+5\right)\left(2000+10\right)+.......+\left(1000+1010\right)\)
\(\Leftrightarrow\) \(2010.\dfrac{2005}{5}=2010.401=405010\)
c) \(140+136+132+.......+64+60\)
\(\Leftrightarrow\) \(\left(140+60\right)+\left(136+64\right)+.......+\left(100+100\right)\)
\(\Leftrightarrow\) \(200.10\) = \(2000\)
1)
a) \(1+2+3+4+.....+2005+2006\)
Số các số hạng của dãy trên là:
\((2006-1):1+1=2006\)
Tổng dãy là:
\(\dfrac{2006\left(2006+1\right)}{2}=2013021\)
b) \(5+10+15+.....+2000+2005\)
Số các số hạng của dãy là:
\((2005-5):5+1=401\)
Tổng dãy là:
\(\dfrac{401\left(2005+5\right)}{2}=403005\)
c)\(140+136+132+.....+64+60\)
\(=60+64+.....+132+136+140\)
Số số hạng của dãy là:
\((140-60):4+1=11\)
Tổng dãy là:
\(\dfrac{11\left(60+140\right)}{2}=1100\)
(2x - 3)(x - 3)(x + 3)
=(2x-3)(x2-9)
= 2x3-18x-3x2+27
=2x3-3x2-18x+27
(2x-3)(x-3)(x+3)
=(2x-3)(x\(^2\)-9)
=2x\(^{^{ }3}\)-3x\(^2\)-18x+27
I'm a writer, and I work .....at.......1 home. It doesn't particularly matter where my house is, as long as it is ......a.....3nice house. But last year my wife ......had.......4 a new job in a different part of the country. So, we had to move. This was our first ....experience...5. of .......buying.......6 one house and selling another at the same time. I wouldn' like to do it again. We quickly saw the house ..........which.......7 we wanted. It was then that our problems began: The people who wanted to buy our house couldn't sell .......theirs.....8 and the man whose house we wanted couldn't find a …house…9 he liked. It ......took...10 us nine months to buy the house. Now, I'm not sure if I like it.