`a)`
`3(x-1)=4(1-x)`
`⇔3(x-1)+4(x-1)=0`
`⇔(x-1)(3+4)=0`
`⇔7(x-1)=0`
`⇔x-1=0`
`⇔x=1`
`b)`
`(x-2)(7x+3)=0`
`⇔`\(\left[ \begin{array}{l}x-2=0\\7x+3=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=2\\x=-3/7\end{array} \right.\)
`c)`
`3x-12≥9-4x`
`⇔7x≥21`
`⇔x≥3`
`15`
`(a-b)^2+(b-c)^2+(c-a)^2≥0`
`⇔2a^2+2b^2+2c^2-2ab-2bc-2ac≥0`
`⇔2a^2+2b^2+2c^2≥2ba+2bc+2ac`
`⇔a^2+b^2+c^2≥ab+bc+ac(1)`
\begin{cases} a<b+c\\b<a+c\\c<b+a \end{cases}
⇔\begin{cases} a^2<ab+ac\\b^2<ab+bc\\c^2<cb+ac \end{cases}
`⇒a^2+b^2+c^2<ab+ac+ab+bc+bc+ac`
`⇒a^2+b^2+c^2<2ab+2ac+2cb(2)`
từ `(1);(2)`
`⇒a^2+b^2+c^2≥ab+bc+ac<2ab+2ac+2cb`
