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\(2x^2-7x+5=0\)
\(2x^2-2x-5x+5=0\)
\(2x\left(x-1\right)-5\left(x-1\right)=0\)
\(\left(x-1\right)\left(2x-5\right)=0\)
\(\left[\begin{array}{nghiempt}x-1=0\\2x-5=0\end{array}\right.\)
\(\left[\begin{array}{nghiempt}x=1\\2x=5\end{array}\right.\)
\(\left[\begin{array}{nghiempt}x=1\\x=\frac{5}{2}\end{array}\right.\)
\(x\left(2x-5\right)-4x+10=0\)
\(x\left(2x-5\right)-2\left(2x-5\right)=0\)
\(\left(2x-5\right)\left(x-2\right)=0\)
\(\left[\begin{array}{nghiempt}x-2=0\\2x-5=0\end{array}\right.\)
\(\left[\begin{array}{nghiempt}x=2\\2x=5\end{array}\right.\)
\(\left[\begin{array}{nghiempt}x=2\\x=\frac{5}{2}\end{array}\right.\)
\(\left(x-5\right)\left(x+5\right)-x\left(x-2\right)=15\)
\(x^2-25-x^2+2x=15\)
\(2x=15+25\)
\(2x=40\)
\(x=\frac{40}{2}\)
\(x=20\)
\(x^2\left(2x-3\right)-12+8x=0\)
\(x^2\left(2x-3\right)+4\left(2x-3\right)=0\)
\(\left(2x-3\right)\left(x^2+4\right)=0\)
\(2x-3=0\) (vì \(x^2\ge0\Rightarrow x^2+4\ge4>0\))
\(2x=3\)
\(x=\frac{3}{2}\)
\(x\left(x-1\right)+5x-5=0\)
\(x\left(x-1\right)+5\left(x-1\right)=0\)
\(\left(x-1\right)\left(x+5\right)=0\)
\(\left[\begin{array}{nghiempt}x-1=0\\x+5=0\end{array}\right.\)
\(\left[\begin{array}{nghiempt}x=1\\x=-5\end{array}\right.\)
\(\left(2x-3\right)^2-4x\left(x-1\right)=5\)
\(4x^2-12x+9-4x^2+4x=5\)
\(-8x=5-9\)
\(-8x=-4\)
\(x=\frac{4}{8}\)
\(x=\frac{1}{2}\)
\(x\left(5-2x\right)+2x\left(x-1\right)=13\)
\(5x-2x^2+2x^2-2x=13\)
\(3x=13\)
\(x=\frac{13}{3}\)
\(2\left(x+5\right)\left(2x-5\right)+\left(x-1\right)\left(5-2x\right)=0\)
\(\left(2x+10\right)\left(2x-5\right)-\left(x-1\right)\left(2x-5\right)=0\)
\(\left(2x-5\right)\left(2x+10-x+1\right)=0\)
\(\left(2x-5\right)\left(x+11\right)=0\)
\(\left[\begin{array}{nghiempt}2x-5=0\\x+11=0\end{array}\right.\)
\(\left[\begin{array}{nghiempt}2x=5\\x=-11\end{array}\right.\)
\(\left[\begin{array}{nghiempt}x=\frac{5}{2}\\x=-11\end{array}\right.\)

đây là 1 hằng đẳng thức luôn
\(=\left(2x-3-2x-5\right)^2=\left(-8\right)^2=64\)

Bài làm:
Ta có:
\(\left(2x+3\right)^2+\left(5-2x\right)\left(5+2x\right)\)
\(=4x^2+12x+9+25-4x^2\)
\(=12x+34\)
\(4x\left(x-1\right)-\left(2x+5\right)^2\)
\(=4x^2-4x-4x^2-20x-25\)
\(=-24x-25\)
\(\left(7x^2-3\right)\left(x+2\right)-\left(2x+1\right)^2\)
\(=7x^3+14x^2-3x-6-4x^2-4x-1\)
\(=7x^3+10x^2-3x-7\)
\(\left(2x+3\right)^2+\left(5-2x\right)\left(5+2x\right)\)
\(=4x^2+6x+6x+9+25-4x^2\)
\(=12x+34\)
\(4x\left(x-1\right)-\left(2x+5\right)^2\)
\(=4x^2-4x-\left(4x^2+10x+10x+25\right)\)
\(=4x^2-4x-4x^2-20x-25\)
\(=-24x-25\)
\(\left(7x^2-3\right)\left(x+2\right)-\left(2x+1\right)^2\)
\(=7x^3+14x^2-3x-6-\left(4x^2+2x+2x+1\right)\)
\(=7x^3+14x^2-3x-6-4x^2-4x-1\)
\(=7x^3+10x^2-7x-7\)

\(\Leftrightarrow\left(2x+3-2x+5\right)^2=x^2+6x+64\)
=>x^2+6x=0
=>x(x+6)=0
=>x=0 hoặc x=-6

Đặt \(y = 2x - 5\).
\(\begin{array}{l}\left[ {8{x^3}{{\left( {2x - 5} \right)}^2} - 6{x^2}{{\left( {2x - 5} \right)}^3} + 10x{{\left( {2x - 5} \right)}^2}} \right]:2x{\left( {2x - 5} \right)^2}\\ = \left( {8{x^3}.{y^2} - 6{x^2}.{y^3} + 10x.{y^2}} \right):2x{y^2}\\ = 8{x^3}.{y^2}:2x{y^2} - 6{x^2}.{y^3}:2x{y^2} + 10x.{y^2}:2x{y^2}\\ = 4{x^2} - 3xy + 5\\ = 4{x^2} - 3x\left( {2x - 5} \right) + 5\\ = 4{x^2} - 6{x^2} + 15x + 5\\ = - 2{x^2} + 15x + 5\end{array}\)
Hồ Thị Thu Thảo cách làm của cậu sai rồi.