a)
`3/4x-x^2=0`
`⇔x(3/4-x)=0`
⇔\(\left[ \begin{array}{l}x=0\\\frac{3}{4}-x=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=0\\x=\frac{3}{4}\end{array} \right.\)
b)
`x^2-8x-9=0`
`⇔x^2+x-9x-9=0`
`⇔x(x+1)-9(x+1)=0`
`⇔(x-9)(x+1)=0`
⇔\(\left[ \begin{array}{l}x-9=0\\x+1=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=9\\x=-1\end{array} \right.\)
c)
`2x^2-7x+5=0`
`⇔2x^2-2x-5x+5=0`
`⇔2x(x-1)-5(x-1)=0`
`⇔(2x-5)(x-1)=0`
⇔\(\left[ \begin{array}{l}2x-5=0\\x-1=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=\frac{5}{2}\\x=1\end{array} \right.\)
d)
`4x-9x^2+5=0`
`⇔9x^2-4x-5=0`
`⇔9x^2-9x+5x-5=0`
`⇔9x(x-1)+5(x-1)=0`
`⇔(9x+5)(x-1)=0`
⇔\(\left[ \begin{array}{l}9x+5=0\\x-1=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=\frac{-5}{9}\\x=1\end{array} \right.\)
e)
`x^2-x+1=0`
`⇔x^2-x+1/4+3/4=0`
`⇔x^2-1/2x-1/2x+1/4+3/4=0`
`⇔x(x-1/2)-1/2(x-1/2)+3/4=0`
`⇔(x-1/2)^2=-3/4` (Vô lý)
⇔Đa thức vô nghiệm
