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1a) -3x2(2x3 - 2x + 1/3) = -6x5 + 6x3 - x2
b) (x4 + 2x3 - 2/3).(-3x4) = -3x8 - 6x7 + 2x4
c) (x + 3)(x - 4) = x2 - 4x + 3x - 12 = x2 - x - 12
d)(x - 4)(x2 + 4x + 16) = (x - 4)(x2 + 4x + 42) = x3 - 64
e) 4(x - 1/2)(x + 1/2)(4x2 + 1) =4(x2 - 1/4)(4x2 + 1) = 4(4x4 + x2 - x2 - 1/4) = 4(4x4 - 1/4) = 16x4 - 1
B2. a) (2 - x)(x2 + 2x + 4) + x(x - 3)(x + 4) - x2 + 24 = 0
=> 8 - x3 + x(x2 + 4x - 3x - 12) - x2 + 24 = 0
=> 8 - x3 + x3 + x2 - 12x - x2 + 24 = 0
=> -12x + 32 = 0
=> -12x = -32
=> x = -32 : (-12) = 8/3
b) (x/2 + 3)(5 - 6x) + (12x - 2)(x/4 + 3) = 0
=> 5x/2 - 3x2 + 15 - 18x + 3x2 + 36x - x/2 - 6 = 0
=> 20x + 9 = 0
=> 20x = -9
=> x = -9/20
a) \(\dfrac{x+5}{4}-\dfrac{x}{2}+1=0\)
<=> \(\dfrac{x+5-2x+4}{4}=0\)
<=> -x + 9 = 0 <=> x = 9
b) \(3\left(x+2\right)=\dfrac{x-4}{3}\)
<=> 9x + 18 = x-4
<=> 8x = -22
<=> x = \(\dfrac{-11}{4}\)
1.
\(y'=12x+\dfrac{4}{x^2}\)
2.
\(y'=\dfrac{3}{\left(-x+1\right)^2}\)
3.
\(y'=\dfrac{2x-3}{2\sqrt{x^2-3x+4}}\)
4.
\(y=\dfrac{x^3+3x^2-x-3}{x-4}\)
\(y'=\dfrac{\left(3x^2+6x-1\right)\left(x-4\right)-\left(x^3+3x^2-x-3\right)}{\left(x-4\right)^2}=\dfrac{2x^3-9x^2-24x+7}{\left(x-4\right)^2}\)
5.
\(y'=-\dfrac{4x-3}{\left(2x^2-3x+5\right)^2}\)
6.
\(y'=\sqrt{x^2-1}+\dfrac{x\left(x+1\right)}{\sqrt{x^2-1}}\)
Bài 1: Đặt \(f\left(x\right)=\left(x^2+x+1\right)^{10}+\left(x^2-x+1\right)^{10}-2\)
Giả sử \(f\left(x\right)\)chia hết cho x-1
\(\Rightarrow f\left(x\right)=\left(x-1\right)q\left(x\right)\)
\(\Rightarrow f\left(1\right)=\left(1-1\right)q\left(1\right)\)
\(=0\)
\(\Leftrightarrow\left(1^2+1+1\right)^{10}+\left(1^2-1+1\right)^{10}-2=0\)
Mà \(\left(1^2+1+1\right)^{10}+\left(1^2-1+1\right)^{10}-2=59048\)
\(\Rightarrow\)mâu thuẫn
\(\Rightarrow f\left(x\right)\)không chia hết cho x-1 ( trái với đề bài )
Bài 2:
Vì \(x^4-x^3-3x^2+ax+b\)chia cho \(x^2-x-2\)dư \(2x-3\)
\(\Rightarrow\left(a-1\right)x+b-2=2x-3\)
Đồng nhất hệ số 2 vế ta được:
\(\hept{\begin{cases}a-1=2\\b-2=-3\end{cases}\Leftrightarrow}\hept{\begin{cases}a=3\\b=-1\end{cases}}\)
Vậy ...
Bài 3:
Vì \(P\left(x\right)\)chia \(x+3\)dư 1
\(\Rightarrow P\left(x\right)=\left(x+3\right)q\left(x\right)+1\)
\(\Rightarrow q\left(-3\right)=\left(-3+3\right)q\left(-3\right)+1\)
\(=1\left(1\right)\)
Vì \(P\left(x\right)\)chia \(x-4\)dư 8
\(\Rightarrow P\left(x\right)=\left(x-4\right)q\left(x\right)+8\)
\(\Rightarrow P\left(4\right)=\left(4-4\right)q\left(4\right)+8\)
\(=8\left(2\right)\)
Vì \(P\left(x\right)\)chia cho \(\left(x+3\right)\left(x-4\right)\)được thương là 3x và còn dư
\(\Rightarrow P\left(x\right)=\left(x+3\right)\left(x-4\right)3x+ax+b\left(3\right)\)
Từ (1) , (2) và (3) \(\Rightarrow\hept{\begin{cases}-3a+b=1\\4a+b=8\end{cases}\Leftrightarrow\hept{\begin{cases}-12a+3b=4\\12a+3b=24\end{cases}\Leftrightarrow}\hept{\begin{cases}b=4\\a=1\end{cases}\left(4\right)}}\)
Thay (4) vào (3) ta được:
\(P\left(x\right)=\left(x+3\right)\left(x-4\right)3x+x+4\)
\(\Leftrightarrow P\left(x\right)=3x^3-3x^2-20x+4\)
Mình giải phần 1 ) thôi
\(1)\)
\(a)\frac{3}{2}x-\frac{1}{3}=1-x\)
\(\Rightarrow\frac{3}{2}x+x=1-\frac{1}{3}\)
\(\Rightarrow\frac{5}{2}x=\frac{2}{3}\)
\(\Rightarrow x=\frac{2}{3}:\frac{5}{2}\)
\(\Rightarrow x=\frac{2}{3}.\frac{2}{5}\)
\(\Rightarrow x=\frac{4}{15}\)
b ) \(\left(\frac{1}{3}+x\right)^3=27\)
\(\Rightarrow\frac{1}{3}+x=3\)
\(\Rightarrow x=3-\frac{1}{3}\)
\(\Rightarrow x=\frac{9}{3}-\frac{1}{3}\)
\(\Rightarrow x=\frac{8}{3}\)
Chúc bạn học tốt !!!
Bài 6:
a2+b2=(a+b)2-2ab
<=> 2010 =36-2ab
<=>ab=-987
M=a3+b3
=(a+b)(a2-ab+b2)
=6(a2+987+b^2)
=6(2010+987)
=17982
A) \(\frac{3}{2}\times\frac{4}{5}-x=\frac{2}{3}\)
\(\frac{6}{5}-x=\frac{2}{3}\)
\(x=\frac{6}{5}-\frac{2}{3}\)
\(x=\frac{8}{15}\)
b) \(x\times3\frac{1}{3}=3\frac{1}{3}\div4\frac{1}{4}\)
\(x\times\frac{10}{3}=\frac{10}{3}\div\frac{17}{4}\)
\(x\times\frac{10}{3}=\frac{40}{51}\)
\(x=\frac{40}{51}\div\frac{10}{3}\)
\(x=\frac{4}{17}\)
c) \(x+\frac{1}{2}\times\frac{1}{3}=\frac{3}{4}\)
\(x+\frac{1}{6}=\frac{3}{4}\)
\(x=\frac{3}{4}-\frac{1}{6}\)
\(x=\frac{7}{12}\)
~ HOK TỐT ~
a ) 3/2 x 4/5 - x = 2/3
6/5 - x = 2/3
- x = 2/3 - 6/5
- x = 10/15 - 18/15
- x = -8/15
x = 8/15
b ) x * 31/3 = 31/3 : 41/4
x * 31/3 = 124/123
x = 124/123 : 31/3
x = 4/41
c ) x + 1/2 x 1/3 = 3/4
x + 1/6 = 3/4
x = 3/4 - 1/6
x = 9/12 - 2/12
x = 7/12