Question

Qual é a soma das raízes da equação (x-2)(3x+1)= (3x-2) (1-x) =

Answer 1

$(x-2)(3x+1)= (3x-2) (1-x) \\\\\\ 3 x^{2} +x-6x-2=3x-3 x^{2} -2+2x\to \\\\ 3 x^{2} +x-6x-2-3x+3 x^{2} +2-2x=0\to\\\\ 3 x^{2} + 3 x^{2} +x-6x-3x-2x-2+2=0\to \\\\\\ 6 x^{2} -10x=0\\\\\\ x(6x-10)=0\to \\\\ x=0\\\\ 6x-10=0\to 6x=10\to x= \frac{10}{6} \to x= \frac{5}{3} \\\\\\\\ S=(0; \frac{5}{3})$


$0+ \frac{5}{3}= \frac{5}{3}$

R.: A soma das raízes dessa equação é igual a $\frac{5}{3}$.