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A.(2x-5)=2x3-7x2+9x-10
\(\Rightarrow\)A = 2x3-7x2+9x-10 : (2x-5)
Bạn thực hiện chia đa thức cho đa thức được bao nhiêu đó là A
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a) Ta có: \(3x-5+7x=17-2x+8\)
\(\Leftrightarrow10x-5=25-2x\)
\(\Leftrightarrow10x-5-25+2x=0\)
\(\Leftrightarrow12x-30=0\)
\(\Leftrightarrow12x=30\)
\(\Leftrightarrow x=\frac{30}{12}=\frac{5}{2}\)
Vậy: \(x=\frac{5}{2}\)
b) Ta có: \(13-5x+14=3x-17-9x\)
\(\Leftrightarrow27-5x=-17-6x\)
\(\Leftrightarrow27-5x+17+6x=0\)
\(\Leftrightarrow44+x=0\)
\(\Leftrightarrow x=-44\)
Vậy: x=-44
c) Ta có: \(x-12+4x=25+2x-49\)
\(\Leftrightarrow x-12+4x-25-2x+49=0\)
\(\Leftrightarrow3x+12=0\)
\(\Leftrightarrow x=-4\)
Vậy: x=-4
d) Ta có: \(7x+10+5=3\left(2x-3\right)-9x\)
\(\Leftrightarrow7x+15=6x-9-9x\)
\(\Leftrightarrow7x+15-6x+9+9x=0\)
\(\Leftrightarrow10x+24=0\)
\(\Leftrightarrow10x=-24\)
\(\Leftrightarrow x=-\frac{24}{10}=\frac{-12}{5}\)
Vậy: \(x=-\frac{12}{5}\)
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a) \(x^2+7x+12\)
\(=x^2+3x+4x+12\)
\(=x\left(x+3\right)+4\left(x+3\right)\)
\(=\left(x+3\right)\left(x+4\right)\)
b) \(3x^2-5x+2\)
\(=3x^2-3x-2x+2\)
\(=3x\left(x-1\right)-2\left(x-1\right)\)
\(=\left(x-1\right)\left(3x-2\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) x2 - 7x + 5 = ( x2 - 2 . 7/2 . x + 49 / 4 ) + 5 - 49 / 4
= (x - 7/2)^2 - 29/4
= (x - 7/2)^2 - (√ 29 / 2 )^2
= ( x - ( 7 + √ 29 / 2 )). ( x + ( 7 - √ 29 / 2 ))
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20) -5-(x + 3) = 2 - 5x ⇔ -5 - x - 3 = 2 -5x ⇔ 4x = 10 ⇔ x = \(\frac{5}{2}\)
Vậy...
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\(\frac{x+1}{x-2}+\frac{x-1}{x+2}=\frac{2\left(x^2+2\right)}{x^2-4}\left(x\ne\pm2\right)\)
\(\Leftrightarrow\frac{\left(x+1\right)\left(x+2\right)+\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=\frac{2\left(x^2+2\right)}{x^2-4}\)
\(\Leftrightarrow\frac{2x^2+4}{x^2-4}=\frac{2x^2+4}{x^2-4}\)
Vậy phương trình này có vô số nghiệm x thỏa mãn trừ x khác 2 và -2
![](https://rs.olm.vn/images/avt/0.png?1311)
a,(2x-3)^2-(2x-3)(x+1)=0
(2x-3)(2x-3-x-1)=0
(2x-3)(x-4)=0
2x-3=0 or x-4=0
x=3/2 or x=4
Ta có: \(\dfrac{2x^3-7x^2+9x-10}{2x-5}\)
\(=\dfrac{2x^3-5x^2-2x^2+5x+4x-10}{2x-5}\)
\(=\dfrac{x^2\left(2x-5\right)-x\left(2x-5\right)+2\left(2x-5\right)}{2x-5}\)
\(=x^2-x+2\)
Chịu