(\(x^2-3x+2\)). (\(x^2+9x+20\)) =112
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20 tháng 6 2021
$ a/ 12x(x – 5) – 3x(4x - 10) = 120$
`<=>12x^2-60x-12x^2+30x=120`
`<=>-30x=120`
`<=>x=-4`
Vậy `x=-4`
$b/ 9x(x + 4) – 5x(3x + 2) = 112 - 2x(3x + 1)$
`<=>9x^2+36x-15x^2-10x=112-6x^2-2x`
`<=>-6x^2+26x=112-6x^2-2x`
`<=>28x=112`
`<=>x=4`
Vậy `x=4`
$c/ 3x(1 – x) - 5x(3x + 7) = 154 + 9x(5 – 2x)$
`<=>3x-3x^2-15x^2-35x=154+45x-18x^2`
`<=>-32x-18x^2=154+45x-18x^2`
`<=>77x=-154`
`<=>x=-2`
Vậy `x=-2`
MC
1
11 tháng 12 2015
1)/3x+1/-5=2
/3x+1/=2+5
/3x+1/=7
/3x/=7-1
/3x/=6
/x/=6:3
/x/=2
=>x=2 hoặc x=-2
2)-112-9x=-200
9x=-112--200
9x=108
x=108:9
x=12
tick nha
LT
4
2 tháng 12 2023
bài 5:
1: \(\dfrac{12x^3y^2}{18xy^5}=\dfrac{12x^3y^2:6xy^2}{18xy^5:6xy^2}=\dfrac{2x^2}{3y^3}\)
2: \(\dfrac{10xy-5x^2}{2x^2-8y^2}=\dfrac{5x\cdot2y-5x\cdot x}{2\left(x^2-4y^2\right)}\)
\(=\dfrac{5x\left(2y-x\right)}{-2\left(x+2y\right)\left(2y-x\right)}=\dfrac{-5x}{2\left(x+2y\right)}\)
3: \(\dfrac{x^2-xy-x+y}{x^2+xy-x-y}\)
\(=\dfrac{\left(x^2-xy\right)-\left(x-y\right)}{\left(x^2+xy\right)-\left(x+y\right)}\)
\(=\dfrac{x\left(x-y\right)-\left(x-y\right)}{x\left(x+y\right)-\left(x+y\right)}=\dfrac{\left(x-y\right)\left(x-1\right)}{\left(x+y\right)\left(x-1\right)}=\dfrac{x-y}{x+y}\)
4: \(\dfrac{\left(x+1\right)\left(x^2-2x+1\right)}{\left(6x^2-6\right)\left(x^3-1\right)}\)
\(=\dfrac{\left(x+1\right)\left(x-1\right)^2}{6\left(x^2-1\right)\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{\left(x+1\right)\left(x-1\right)}{6\left(x-1\right)\left(x+1\right)\cdot\left(x^2+x+1\right)}\)
\(=\dfrac{1}{6\left(x^2+x+1\right)}\)
5: \(\dfrac{2x^2-7x+3}{1-4x^2}\)
\(=-\dfrac{2x^2-7x+3}{4x^2-1}\)
\(=-\dfrac{2x^2-6x-x+3}{\left(2x-1\right)\left(2x+1\right)}\)
\(=-\dfrac{2x\left(x-3\right)-\left(x-3\right)}{\left(2x-1\right)\left(2x+1\right)}\)
\(=-\dfrac{\left(x-3\right)\left(2x-1\right)}{\left(2x-1\right)\left(2x+1\right)}=\dfrac{-x+3}{2x+1}\)
Bài 3:
1: \(9x^3-xy^2\)
\(=x\cdot9x^2-x\cdot y^2\)
\(=x\left(9x^2-y^2\right)\)
\(=x\left(3x-y\right)\left(3x+y\right)\)
2: \(x^2-3xy-6x+18y\)
\(=\left(x^2-3xy\right)-\left(6x-18y\right)\)
\(=x\left(x-3y\right)-6\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x-6\right)\)
3: \(x^2-3xy-6x+18y\)
\(=\left(x^2-3xy\right)-\left(6x-18y\right)\)
\(=x\left(x-3y\right)-6\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x-6\right)\)
4: \(6xy-x^2+36-9y^2\)
\(=36-\left(x^2-6xy+9y^2\right)\)
\(=36-\left(x-3y\right)^2\)
\(=\left(6-x+3y\right)\left(6+x-3y\right)\)
5: \(x^4-6x^2+5\)
\(=x^4-x^2-5x^2+5\)
\(=x^2\left(x^2-1\right)-5\left(x^2-1\right)\)
\(=\left(x^2-5\right)\left(x^2-1\right)\)
\(=\left(x^2-5\right)\left(x-1\right)\left(x+1\right)\)
6: \(9x^2-6x-y^2+2y\)
\(=\left(9x^2-y^2\right)-\left(6x-2y\right)\)
\(=\left(3x-y\right)\left(3x+y\right)-2\left(3x-y\right)\)
\(=\left(3x-y\right)\left(3x+y-2\right)\)
AH
Akai Haruma
Giáo viên
19 tháng 10 2018
\(B=\frac{x^2+10x+20}{x^2+6x+9}=\frac{(x^2+6x+9)+4(x+3)-1}{x^2+6x+9}\)
\(=1+\frac{4(x+3)}{x^2+6x+9}-\frac{1}{x^2+6x+9}=1+\frac{4(x+3)}{(x+3)^2}-\frac{1}{(x+3)^2}\)
\(=1+\frac{4}{(x+3)}-\frac{1}{(x+3)^2}\)
Đặt \(\frac{1}{x+3}=a\Rightarrow B=1+4a-a^2=5-(a^2-4a+4)\)
\(=5-(a-2)^2\leq 5\)
Vậy \(B_{\max}=5\Leftrightarrow a=2\Leftrightarrow x=-\frac{5}{2}\)
AH
Akai Haruma
Giáo viên
19 tháng 10 2018
\(C=\frac{3x^2+9x+17}{3x^2+9x+7}=\frac{3x^2+9x+7+10}{3x^2+9x+7}=1+\frac{10}{3x^2+9x+7}\)
Có: \(3x^2+9x+7=3(x^2+3x+\frac{9}{4})+\frac{1}{4}=3(x+\frac{3}{2})^2+\frac{1}{4}\geq \frac{1}{4}\)
\(\Rightarrow \frac{10}{3x^2+9x+7}\leq \frac{10}{\frac{1}{4}}=40\)
\(\Rightarrow C\leq 41\)
Vậy \(C_{\max}=41\Leftrightarrow x=\frac{-3}{2}\)
9 tháng 10 2022
\(\Leftrightarrow\left(x^2-3x+1\right)\left(x+1\right)\left(x+2\right)\left(x-4\right)\left(x-5\right)=-30\)
\(\Leftrightarrow\left(x^2-3x+1\right)\left(x^2-3x-4\right)\left(x^2-3x-5\right)=-30\)
Đặt x^2-3x=a
=>(a+1)(a-4)(a-5)=-30
=>\(\left(a^2-3a-4\right)\left(a-5\right)=-30\)
=>\(a^3-5a^2-3a^2+15a-4a+20+30=0\)
=>a^3-8a^2+11a+50=0
=>a=-1,77
=>x^2-3x=-1,77
=>x^2-3x+1,77=0
hay \(\left[{}\begin{matrix}x=\dfrac{15+4\sqrt{3}}{10}\\x=\dfrac{15-4\sqrt{3}}{10}\end{matrix}\right.\)
FT
1
2 tháng 11 2016
\(\left(x^2-3x+2\right)\left(x^2-9x+20\right)-40=\left(x-1\right)\left(x-2\right)\left(x-4\right)\left(x-5\right)-40\)
\(=\left(x^2-6x+5\right)\left(x^2-6x+8\right)-40\)
Đặt \(t=x^2-6x+5\) thì ta có \(t\left(t+3\right)-40=t^2+3t-40=\left(t+8\right)\left(t-5\right)\)
Suy ra \(\left(x^2-6x+5\right)\left(x^2-6x+8\right)-40=\left(x^2-6x+13\right)\left(x^2-6x\right)=x\left(x-6\right)\left(x^2-6x+13\right)\)
\(\left(x-1\right)\left(x-2\right)\left(x+4\right)\left(x+5\right)=112\)
\(\left(x^2+3x-4\right)\left(x^2+3x-10\right)=112\)
Đặt \(t=x^2+3x-4\)
\(t\left(t-6\right)=112\Rightarrow t^2-6t-112=0\Leftrightarrow\left(t+8\right)\left(t-14\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x^2+3x-4=-8\\x^2+3x-4=14\end{cases}\Rightarrow\orbr{\begin{cases}\left(l\right)\\x=3,x=-6\end{cases}}}\)