(x+1)(x+2)(x+3)(x+4) - 40
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1:
\(\Leftrightarrow\left(x^2+5x+6\right)\left(x^2+5x+4\right)=24\)
\(\Leftrightarrow\left(x^2+5x\right)^2+10\left(x^2+5x\right)=0\)
\(\Leftrightarrow x^2+5x=0\)
=>x=0 hoặc x=-5
3: \(\Leftrightarrow\left(x^2+x+6\right)\left(x^2+x-2\right)=0\)
=>(x+2)(x-1)=0
=>x=-2 hoặc x=1
\(A=\left(x+1\right)^3-\left(x+3\right)^2\left(x+1\right)+4x^2+8\)
\(A=x^3+3x^2+3x+1-\left(x^2+6x+9\right)\left(x+1\right)+4x^2+8\)
\(A=x^3+3x^2+3x+1-\left(x^3+6x^2+9x+x^2+6x+9\right)+4x^2+8\)
\(A=x^3+3x^2+3x+1-x^3-6x^2-9x-x^2-6x-9+4x^2+8\)
\(A=\left(x^3-x^3\right)+\left(3x^2-6x^2-x^2+4x^2\right)+\left(3x-9x-6x\right)+\left(1-9+8\right)\)
\(A=-12x\)
\(B=\left(x-2\right)\left(x^2+2x+4\right)-\left(x+1\right)^3+3\left(x-1\right)\left(x+1\right)\)
\(B=x^3+2x^2+4x-2x^2-4x-8-\left(x^3+3x^2+3x+1\right)+3\left(x^2-1\right)\)
\(B=x^3+2x^2+4x-2x^2-4x-8-x^3-3x^2-3x-1+3x^2-3\)
\(B=\left(x^3-x^3\right)+\left(2x^2-2x^2-3x^2+3x^2\right)+\left(4x-4x-3x\right)+\left(-8-3-1\right)\)
\(B=-3x-12\)
Câu C tương tự.
Chúc bạn học tốt!!!
A = \(\left(x+1\right)^3-\left(x+3\right)^2.\left(x+1\right)+4x^2+8\)
A = \(\left(x+1\right)\left(x+1-x-3\right)\left(x+1+x+3\right)+4x^2+8\)
A = \(\left(x+1\right).\left(-2\right).\left(2x+4\right)+4x^2+8\)
A = \(\left(-2\right)\left(2x^2+4x+2x+4\right)+4x^2+8\)
A = \(\left(-2\right)\left(2x^2+6x+4\right)+4x^2+8\)
A = \(-4x^2-12x-8+4x^2+8=-12x\)
b) B = \(\left(x-2\right)\left(x^2+2x+4\right)-\left(x+1\right)^3+3\left(x-1\right)\left(x+1\right)\)
B = \(x^3-8-\left(x+1\right)\left(x^2+2x+1+3x-3\right)\)
B = \(x^3-8-\left(x+1\right)\left(x^2+5x-2\right)\)
B = \(x^3-8-x^3-5x^2+2x-x^2-5x+2\)
B = \(-6x^2-3x-6\)
HOC24 có câu rất hay :Người hay giúp bạn khác trả lời bài tập sẽ trở thành học sinh giỏi. Người hay hỏi bài thì không. Còn bạn thì sao? đúng tính bà đó . Lên lớp đừng đập nha :)
a) 3 . ( 1/2 - x ) + 1/3 = 7/6 - x
=> 3/2 - 3x + 1/3 = 7/6-x
=> -3x +x=7/6 - 3/2 - 1/3
=> -2x = -2/3
=> x=-2/3 : (-2) = 1/3
hết :)
1)
\(\left(x+1\right)\left(x+2\right)\left(x+4\right)\left(x+5\right)=40\)
\(\Leftrightarrow\left(x+1\right)\left(x+5\right).\left(x+2\right)\left(x+4\right)-40=0\)
\(\Leftrightarrow\left(x^2+6x+5\right).\left(x^2+6x+8\right)-40=0\)
Đặt \(a=x^2+6x+6\) ta có:
\(\Leftrightarrow\left(a-1\right)\left(a+2\right)-40=0\)
\(\Leftrightarrow a^2+a-2-40=0\)
\(\Leftrightarrow a^2-6x+7x-42=0\)
\(\Leftrightarrow a\left(a-6\right)+7\left(a-6\right)=0\)
\(\Leftrightarrow\left(a-6\right)\left(a+7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=6\\a=-7\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+6x+6=6\\x^2+6x+6=-7\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+6x=0\\x^2+6x+13=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-6\\x=0\end{matrix}\right.\)
(\(x^2+6x+13=\left(x+3\right)^2+4>0\left(loại\right)\))
Vậy.................
3)
\(\left|x+4\right|=\left|3-2x\right|\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=3-2x\\x+4=-3+2x\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+1=0\\-x+7=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-1}{3}\\x=7\end{matrix}\right.\)
Vậy..........
mình làm câu a) (1/2 + 1 ) x ( 1/3 + 1 ) x ( 1/4 + 1 ) x....x (1/999 + 1 )
=>\(\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}....\dfrac{999}{998}.\dfrac{1000}{998}\)
=>\(\dfrac{3.4.5...999.1000}{2.3.4...997.998}\)
=> \(\dfrac{1000}{2}\) = 500
minh lam cau b
\(\dfrac{-1}{2}\cdot\dfrac{-2}{3}\cdot\cdot\cdot\cdot\cdot\dfrac{-999}{1000}\)
vi tu 1-999 co so cac so la le nen gia tri la so am
Neu tu la duong thi ta co :
\(\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\cdot\cdot\cdot\cdot\dfrac{999}{1000}\\ =\dfrac{1}{1000}\)
Nhung tu so phai la am \(\Rightarrow\)\(\dfrac{1}{1000}\) se phai la\(\dfrac{-1}{1000}\)
Vay dap an la \(\dfrac{-1}{1000}\)
S = 1 x 2 + 2 x 3 + 3 x 4 + 4 x 5 + ... + 39 x 40
3S = 1 x 2 x 3 + 2 x 3 x 3 + 3 x 4 x 3 + 4 x 5 x 3 + ... + 39 x 40 x 3
3S = 1x2x3 + 2x3x(4-1 ) + 3x4x(5-2 ) + 4x5x(6-3 ) + ... + 39x40x(41-38 )
3S = 1 x 2x3 + 2x3x4-1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 39x40x31 - 38x39x40
3S = 39x40x41
S = 39x40x41 : 3
S = 21320
S=1*2+ 2*3 + 3*4 +.....+ 39*40
S= 2 + 6+ 12 + ....+ 1560
S= 2 + 0 + 4 + 2 +6 + 4 + 2+ ....... + 1554 + 4 +2
S= 2 + 0 + 6 +6 + 6 + ....... +1554 + 6
S= 2 + ( 0 + 6 + ..... +1554)+ ( 6 * ((1554-0):6+1))
S = 2 + 202020 + 1560
S = 203582
( x + 1) + )+ ( x + 2) +( x + 3) +) + ( x + 4 ) + ( x + 5 ) = 40
( x+x+x+x+x ) + ( 1+2+3+4+5 ) = 40
x*5 + 15 = 40
x*5 = 40-15
x*5 = 25
x= 25 :5
x=5
x+1+x+2+x+3+x+4+x+5=40
5*x+(1+2+3+4+5) =40
5*x+15 =40
5*x =40-15
5*x =25
x =25/5
x =5
\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)=40\\ \Leftrightarrow\left[\left(x+1\right)\left(x+4\right)\right]\left[\left(x+2\right)\left(x+3\right)\right]=40\\ \Leftrightarrow\left(x^2+5x+4\right)\left(x^2+5x+6\right)=40\\ \Leftrightarrow\left(x^2+5x+4\right)\left[\left(x^2+5x+4\right)+2\right]=40\\ \Leftrightarrow\left(x^2+5x+4\right)^2+2\left(x^2+5x+4\right)-40=0\)
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