Question

A solução da equação x(x-1)=-2(x-4)-2 é:

a) S= {4,3}
b) S= {2,3}
c) S= {-3,2}
d) S= {4,3}

Answer 1

$x(x-1)=-2(x-4)-2 \\ \\ x^2-x=-2x+8-2 \\ \\ x^2-x+2x-8+2=0 \\ \\ x^{2} +x-6=0 \\ \\ a=1 \\ b=1 \\ c=-6 \\ \\ \Delta=b^2-4ac \\ \Delta=1^2-4(1)(-6) \\ \Delta=1+24 \\ \Delta=25 \\ \\ x= \frac{-b\pm \sqrt{\Delta} }{2a} \\ \\ x= \frac{-1\pm \sqrt{25} }{2} = \frac{-1\pm5}{2} \\ \\ x'= \frac{-1-5}{2} =- \frac{6}{2} =-3 \\ \\ x"= \frac{-1+5}{2} = \frac{4}{2} =2 \\ \\ S=\{-3,2\} \mapsto~Letra~~C$