Question

Quais as raízes da equação x + x²=90

Answer 1

Resposta:

x+x²=90

x²+x-90=0

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}+1x-90=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=1~e~c=-90\\\\\Delta=(b)^{2}-4(a)(c)=(1)^{2}-4(1)(-90)=1-(-360)=361\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(1)-\sqrt{361}}{2(1)}=\frac{-1-19}{2}=\frac{-20}{2}=-10\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(1)+\sqrt{361}}{2(1)}=\frac{-1+19}{2}=\frac{18}{2}=9\\\\S=\{-10,~9\}$