5x(x - 3)(x + 3) - (2x - 3)2 - 5(x + 2) + 34x(x + 2) = 1
\(\Leftrightarrow-\left(2x-3\right)^2+5x\left(x-3\right)\left(x+3\right)+34x\left(x+2\right)-5\left(x+2\right)-1=0\)
\(\Leftrightarrow\left[-\left(2x-3\right)^2+5x\left(x^2-9\right)-1\right]+\left(x+2\right)\left(34x-5\right)=0\)
\(\Leftrightarrow\left(-4x^2+12x-9+5x^3-45x-1\right)+\left(x+2\right)\left(34x-5\right)=0\)
\(\Leftrightarrow\left(5x^3-4x^2-33x-10\right)+\left(x+2\right)\left(34x-5\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(5x^2-14x-5\right)+\left(x+2\right)\left(34x-5\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(5x^2-14x-5+34x-5\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(5x^2+20x-10\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x^2+4x-2\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=-2\\x^2+4x-2=0\left(1\right)\end{array}\right.\)
\(\left(1\right)\Leftrightarrow x^2+4x+4-6=0\)
\(\Leftrightarrow\left(x+2\right)^2=6\)
\(\Leftrightarrow x=\pm\sqrt{6}-2\)
Vậy pt có nghiệm là \(\left[\begin{array}{nghiempt}x=-2\\x=\pm\sqrt{6}-2\end{array}\right.\)
