\(\left(3x-2\right)^2-2\left(x-2\right)^2\)

\(=\left(9x^2-12x+4\right)-2\left(x^2-4x+4\right)\)

\(=9x^2-12x+4-2x^2+8x-8\)

\(=7x^2+4x+4\)

abcd=1 đâu ra zậy

\(S=\left(xy+yz+zx\right)\cdot\frac{xy+yz+zx}{xyz}-\frac{xyz\left(x^2y^2+y^2z^2+z^2x^2\right)}{x^2y^2z^2}\)

\(=\frac{\left(xy+yz+zx\right)^2}{xyz}-\frac{x^2y^2+y^2z^2+z^2x^2}{xyz}\)

\(=\frac{x^2y^2+y^2z^2+z^2x^2+2xyz\left(x+y+z\right)-x^2y^2-y^2z^2-z^2x^2}{xyz}\)

\(=\frac{2xyz\left(x+y+z\right)}{xyz}=2\left(x+y+z\right)\)

1,x^2-(x+1)(x-1)=0
x^2-x^2+1+0
1=0(vô lý)
2,5x^3+3x^2+3x+1=4x^2
x^3+3x^2+3x+1=0
(x+1)=0
x=-1
3,x^3+x^2=0
x^2(x+1)=0
x=0 or x=-1
4,2x^3-12x^2+18x=0
x^3-6x^2+9x=0
x(x^2-6x+9)=0
x(x-3)^2=0
x=0 or x=3
5,5x^2-4(x^2-2x+1)+20=0
5x^2-4x^2+8x-4+20=0
x^2+8x+16=0
(x+4)^2=0
x=-4
6,5x(x-3)+7x-21=0
5x(x-3)+7(x-3)=0
(5x+7)(x-3)=0
5x-7=0 or x-3=0
x=7/5 or x=3
7,2x^3-50x=0
2x(x^2-25)=0
2x(x-5)(x+5)=0
x=0 or x=5 or x=-5
8,(4x-1)^2-9(x+3)^2=0
(4x-1)^2-3^2*(x+3)^2=0
(4x-1)^2-(3x+9)^2=0
(4x-1-3x-9)(4x-1+3x+9)=0
(x-10)(7x+8)=0
x=10 or x=-8/7
9,3(x-2)^2-x+2=0
3*(x-2)*(x-2)-(x-2)=0
(3x-6)(x-2)-(x-2)=0
(x-2)(3x-6-1)=0
(x-2)(3x-7)=0
x=2 or x=7/3
10,9x^2+6x-8=0
9x^2+12x-6x-8=0
3x(3x-2)+4(3x-2)=0
(3x+4)(3x-2)=0
3x+4=0 or 3x-2=0
x=-4/3 or x=2/3

\(2\left(3x-1\right)^2-9x+3=0\)

\(\Leftrightarrow\)\(2\left(3x-1\right)^2-3\left(3x-1\right)=0\)

\(\Leftrightarrow\)\(\left(3x-1\right)\left[2\left(3x-1\right)-3\right]=0\)

\(\Leftrightarrow\)\(\left(3x-1\right)\left(6x-5\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}3x-1=0\\6x-5=0\end{cases}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=\frac{1}{3}\\x=\frac{5}{6}\end{cases}}\)

Vậy....

\(5\left(2x-3\right)^2=2x-3\)

\(=20x^2-60x+45=2x-3\)

\(=20x^2-60x+45+3=2x-3+3\)

\(=20x^2-60x+48=2x\)

\(=20x^2-60x+48-2x=2x-2x\)

\(=20x^2-62x+84=0\)

\(=x\in\left\{\frac{8}{5};\frac{3}{2}\right\}\)

\(a,\) \(10a+25+a^2=a^2+10a+25=a^2+2.5.a+5^2=\left(a+5\right)^2\)

\(4m^2+1+4m=4m^2+4m+1=\left(2m\right)^2+2.2m.1+1^2=\left(2m+1\right)^2\)

\(16y^4+9+24y^2=16y^4+24y^2+9=\left(4y^2\right)+2.4y.3+3^2=\left(4y^2+3\right)^2\)

\(b,\)\(36m^2+1-12m=36m^2-12m+1=\left(6m\right)^2-2.6m.1+1^2=\left(6m-1\right)^2\)

\(81z^6+1-18z^3=81z^6-18z^3+1=\left(9z^3\right)^2-2.9z^3.1+1^2=\left(9z^3-1\right)^2\)

Chúc bạn học tốt