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a)
<=> \(3x-12x^2+12x^2-6x=9\)
<=> \(-3x=9\)
<=> \(x=-3\)
b)
<=> \(6x-24x^2-12x+24x^2=6\)
<=> \(-6x=6\)
<=> \(x=-1\)
c)
<=> \(6x-4-3x+6=1\)
<=> \(3x+2=1\)
<=> \(x=-\frac{1}{3}\)
d)
<=> \(9-6x^2+6x^2-3x=9\)
<=> \(-3x=0\)
<=> \(x=0\)
e) KO HIỂU ĐỀ
f)
<=> \(4x^2-8x+3-\left(4x^2+9x+2\right)=8\)
<=> \(-17x+1=8\)
<=> \(x=-\frac{7}{17}\)
g)
<=> \(-6x^2+x+1+6x^2-3x=9\)
<=> \(-2x=8\)
<=> \(x=-4\)
h)
<=> \(x^2-x+2x^2+5x-3=4\)
<=> \(3x^2+4x=7\)
<=> \(\orbr{\begin{cases}x=1\\x=-\frac{7}{3}\end{cases}}\)
a. \(3x\left(1-4x\right)+6x\left(2x-1\right)=9\)
\(\Rightarrow3x-12x^2+12x^2-6x=9\)
\(\Rightarrow-3x=9\)
\(\Rightarrow x=-3\)
b. \(3x\left(2-8x\right)-12x\left(1-2x\right)=6\)
\(\Rightarrow6x-24x^2-12x+24x^2=6\)
\(\Rightarrow-6x=6\)
\(\Rightarrow x=-1\)
c. \(2\left(3x-2\right)-3\left(x-2\right)=1\)
\(\Rightarrow6x-4-3x+6=1\)
\(\Rightarrow3x+2=1\)
\(\Rightarrow3x=-1\)
\(\Rightarrow x=-\frac{1}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,=3\left(x-y\right)\left(x+y\right)\\ b,=2x\left(x^2-25\right)=2x\left(x-5\right)\left(x+5\right)\\ c,=5x\left(x^2-2x+1\right)=5x\left(x-1\right)^2\\ d,=\left(x-y\right)\left(x+y\right)+2\left(x-y\right)=\left(x-y\right)\left(x+y+2\right)\\ e,=x\left(y-3\right)+y\left(y-3\right)=\left(y-3\right)\left(x+y\right)\\ f,=\left(x+2\right)^2-16y^2=\left(x-4y+2\right)\left(x+4y+2\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A = -2x2 - y2 + 2xy + 10x - 6y + 2020
A = -(2x2 + y2 - 2xy - 10x + 6y - 2020)
A = -[(x2 - 2xy + y2) - 6(x - y) + 9 + (x2 - 4x + 4) - 2033)
A = -[(x - y - 3)2 + (x - 2)2] + 2033 < = 2033
Dấu "=" xảy ra <=> \(\hept{\begin{cases}x-y-3=0\\x-2=0\end{cases}}\) <=> \(\hept{\begin{cases}y=x-3\\x=2\end{cases}}\) <=> \(\hept{\begin{cases}y=-1\\x=2\end{cases}}\)
Vậy MaxA = 2033 khi x = 2 và y = -1
B = 150 - x2 + 2xy - 2y2 + 8x - 2y
B = -(x2 - 2xy + 2y2 - 8x + 2y - 150)
B = -[(x2 - 2xy + y2) - 8(x - y) + 16 + (y2 - 6y + 9) - 175]
B = -(x - y - 4)2 - (y - 3)2 + 175 \(\le\)175 \(\forall\)x;y
Dấu "=" xảy ra <=> \(\hept{\begin{cases}x-y-4=0\\y-3=0\end{cases}}\) <=> \(\hept{\begin{cases}x=y+4\\y=3\end{cases}}\) <=> \(\hept{\begin{cases}x=7\\y=3\end{cases}}\)
Vậy MaxB = 175 khi x = 7 và y = 3
![](https://rs.olm.vn/images/avt/0.png?1311)
1: \(=\left(y-1\right)^2\)
2: \(=\left(x+1+5\right)\left(x+1-5\right)=\left(x+6\right)\left(x-4\right)\)
3: =(1-2x)(1+2x)
\(=\left(2-3x\right)\left(4+6x+9x^2\right)\)
5: \(=\left(x+3\right)^3\)
6: \(=\left(2x-y\right)^3\)