\(\left(3x-2\right)^2-4x\left(x-3\right)=\left(5x+1\right)\left(x-4\right).\)

\(\Leftrightarrow9x^2-12x+4-4x^2+12x=5x^2-20x+x-4\)

\(\Leftrightarrow9x^2-12x+4-4x^2+12x=5x^2-20x+x-4\)

\(\Leftrightarrow19x=-8\)

\(\Rightarrow x=-\frac{8}{19}\)

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

\(\Leftrightarrow\left(x+3\right)\left(3x-1\right)=\left(3x-1\right)\left(3x+1\right)\)

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

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

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

Th1 : 3x - 1 = 0

=> x = 1/3

Th2: 2 - 2x = 0

=> x = 1

 A = 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 

A x 3 = 3 x (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729) 

= 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243  A x 3 - A

= 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729) 

= 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - 1/3 - 1/9 - 1/27 - 1/81 - 1/243 - 1/729 

= 1 - 1/729  A x 2

= 728/729 

A = 364/729 

\(a.\frac{x}{2x-6}+\frac{x}{2x+2}-\frac{2x}{\left(x+1\right)\left(x-3\right)}=\)\(0\)

\(\Leftrightarrow\frac{x}{2.\left(x-3\right)}+\frac{x}{2.\left(x+1\right)}-\frac{2x}{\left(x+1\right)\left(x-3\right)}=0\)

\(\Leftrightarrow\frac{x^2+x+x^2-3x-4x}{2.\left(x+1\right).\left(x-3\right)}=0\)

\(\Leftrightarrow2x^2-6=0\)

\(\Leftrightarrow2x^2=6\)

\(\Leftrightarrow x^2=3\)

\(\Leftrightarrow x=\sqrt{3}\)

\(b.2x^3-5x^2+3x=0\)

\(\Leftrightarrow x.\left(2x^2-5x+3\right)=0\)

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

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

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

Đến đây tự làm nhé có việc bận

câu a sai dzoii

https://lazi.vn/edu/exercise/giai-phuong-trinh-x-1-x-22-x-1-x-4-32x-4-x-42-0-1

chỉ tiềm thấy  cái này thôi ~ vì mk k thể giải đc nên nhờ mạng nên thông cảm cho nha

Gọi số vé của GV và HS lần lượt là a,b. Theo đề bài, ta có:

30000a+20000b=3300000(1)

a+b=160(2)

Thay (2) vào (1), ta có:

20000(a+b)+10000a=3300000

20000.160+10000a=3300000

3200000+10000a=3300000

10000a=100000

a=10

=>b=160-a=160-10=150

Vậy có 10 GV và 150 HS

Ta có: \(a^3+b^3+ab=\left(a+b\right)^3-3ab\left(a+b\right)+ab\)

\(=1-3ab+ab=1-2ab=1-2\left(1-b\right)b\)

\(=1-2b+2b^2=2\left(b^2-b+\frac{1}{4}\right)+\frac{1}{2}\)

\(=2\left(b-\frac{1}{2}\right)^2+\frac{1}{2}\ge\frac{1}{2}\)

Đẳng thức xảy ra khi a = b \(=\frac{1}{2}\)