`a, (x-6)(x^2-4)=0`
`⇔`\(\left[ \begin{array}{l}x-6=0\\x^2-4=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=6\\x=±2\end{array} \right.\)
`b, (2x+5)(4x^2-9)=0`
`⇔` \(\left[ \begin{array}{l}2x+5=0\\4x^2-9=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=\dfrac{-5}{2}\\x=±\dfrac{3}{2}\end{array} \right.\)
`c, (x-2)^2 . (x-9)=0`
`⇔`\(\left[ \begin{array}{l}(x-2)^2=0\\x-9=0\end{array} \right.\) `⇔`\(\left[ \begin{array}{l}x=2\\x=9\end{array} \right.\)
`d, x^2 = 2x`
`⇔ x^2 - 2x = 0`
`⇔ x(x -2)=0`
`⇔` \(\left[ \begin{array}{l}x=0\\x-2=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=0\\x=2\end{array} \right.\)
`e, x^2 - 2x + 1 = 4`
`⇔ (x+1)^2 - 4 = 0`
`⇔ (x + 1 - 2)(x + 1 + 2) =0`
`⇔ (x-1)(x+3)=0`
`⇔` \(\left[ \begin{array}{l}x-1=0\\x+3=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=1\\x=-3\end{array} \right.\)
`f, (x^2 + 1)(x - 1)=0`
`⇔` \(\left[ \begin{array}{l}x^2+1=0\\x-1=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x^2=-1(loại)\\x=1\end{array} \right.\)
`g, 4x^2 + 4x + 1 = 0`
`⇔ (2x + 1)^2 = 0`
`⇔ 2x + 1 = 0`
`⇔ x = -1/2`
`h, x^2 - 5x + 6 = 0`
`⇔ x^2 - 3x - 2x + 6 = 0`
`⇔ x(x - 3) - 2(x-3) = 0`
`⇔ (x-2)(x-3)=0`
`⇔` \(\left[ \begin{array}{l}x-2=0\\x-3=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=2\\x=3\end{array} \right.\)
`i, 2x^2 + 3x + 1 =0`
`⇔ 2x^2 + x + 2x + 1 = 0`
`⇔ 2x(x+1) + x +1 =0`
`⇔(2x+1)(x+1)=0`
`⇔` \(\left[ \begin{array}{l}2x+1=0\\x+1=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=\dfrac{-1}{2}\\x=-1\end{array} \right.\)
`j, (2x-3)(x+1)+x(x-2)=3(x+2)^2`
`⇔ 2x^2 +2x-3x-3+x^2-2x-3(x^2+4x+4)=0`
`⇔2x^2 + 2x - 3x - 3 + x^2 - 2x - 3x^2 - 12x - 12=0`
`⇔-15x - 15 = 0`
`⇔x = -1`
