Question

Como resolver este sistema de equações:

$n.x = 180 \\ x = n + 8$
x=18
n=10​

Answer 1

Resposta:

x= -10 e n= -18

ou

x=18 e n=10

Explicação passo-a-passo:

nx=180 => n=180/x

x=n+8 => x=180/x+8 => x²=180+8x => x²-8x-180=0

$\displaystyle\\Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-8x-180=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-8~e~c=-180\\\\\Delta=(b)^{2}-4(a)(c)=(-8)^{2}-4(1)(-180)=64-(-720)=784\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-8)-\sqrt{784}}{2(1)}=\frac{8-28}{2}=\frac{-20}{2}=-10\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-8)+\sqrt{784}}{2(1)}=\frac{8+28}{2}=\frac{36}{2}=18\\\\S=\{-10,~18\}$

para x= -10

n=180/x=180/(-10)= -18

Para x=18

n=180/x=180/18=10