Question

Resolva a equação a seguir (em R).
(x-3).(x + 4) – 10 = (1-x).(x + 2)

Answer 1

Resposta:

Explicação passo-a-passo:

$(x-3).(x + 4)-10 = (1-x).(x + 2)\\\\x^{2}+4x-3x-12-10=x+2-x^{2}-2x\\ \\x^{2}+x-22=2-x^{2}-x\\\\x^{2}+x-22-2+x^{2}+x=0\\\\2x^{2}+2x-24=0$

Dividindo a equação por 2

$x^{2}+x-12=0\\\\\Delta=1^{2}-4.1.(-12)=1+48=49\\\\x=\dfrac{-1\pm\sqrt{49}}{2.1}=\dfrac{-1\pm7}{2}\\\\\\x'=\dfrac{-1+7}{2}=\dfrac{6}{2}=3\\\\\\x''=\dfrac{-1-7}{2}=\dfrac{-8}{2}=-4$