\(a, 3x^2-6x+3=(x-1)(x+4)\)
\(⇔(3x^2-6x+3)-(x-1)(x+4)=0\)
\(⇔3x^2-6x+3-x^2-3x+4=0\)
\(⇔2x^2-9x+7=0\)
\(⇔2x^2-2x-7x+7=0\)
\(⇔2x(x-1)-7(x-1)=0\)
\(⇔(x-1)(2x-7)=0\)
\(⇔\left[\begin{array}{} x-1=0\\ 2x-7=0 \end{array}\right.\)
\(⇔\left[\begin{array}{} x=1\\ x=\dfrac{7}{2} \end{array}\right.\)
Vậy pt có tập nghiệm là S={\(1; \dfrac{7}{2}\)}
\(b, 18x^2(x+4)-12(x^2+4x)=0\)
\(⇔18x^2(x+4)-12x(x+4)=0\)
\(⇔6x(x+4)(3x-2)=0\)
\(⇔\left[\begin{array}{} 6x=0\\\ x+4=0\\ 3x-2=0 \end{array}\right. \)
\(⇔\left[\begin{array}{} x=0\\\ x=-4\\ x=\dfrac{2}{3} \end{array}\right.\)
vậy pt có tập nghiệm là S={\(0;-4;\dfrac{2}{3}\)}
\(c,25x^2-10x+1=2(5x-1)(3x-4)\)
\(⇔(5x-1)^2=(5x-1)(6x-8)\)
\(⇔(5x-1)^2-(5x-1)(6x-8)=0\)
\(⇔(5x-1)[(5x-1)-(6x-8)]=0\)
\(⇔(5x-1)(7-x)=0\)
\(⇔\left[\begin{array}{} 5x-1=0\\ 7-x=0 \end{array}\right.\)
\(⇔\left[\begin{array}{} x=\dfrac{1}{5}\\ x=7 \end{array}\right.\)
Vậy pt có tập nghiệm là S={\(\dfrac{1}{5};7\)}
\(3x^2-6x+3=\left(x-1\right)\left(x+4\right)\\ \Leftrightarrow3x^2-6x+3=x\left(x+4\right)-\left(x+4\right)\\ \Leftrightarrow3x^2-6x+3=x^2+4x-x-4\\ \Leftrightarrow3x^2-6x+3=x^2+3x-4\\ \Leftrightarrow3x^2-6x+3-x^2-3x+4=0\\ \Leftrightarrow2x^2-9x+7=0\\ \Leftrightarrow x\left(2x-9\right)=-7\)
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