Question

sistema de equaçao


x+y=7
x.y=10

Answer 1

Resposta:

x=5 e y=2

ou

x=2 e y=5

Explicação passo-a-passo:

x.y=10 => y=10/x

Substituindo y=10/x em x+y=7

x+10/x=7

(x²+10)/x=(7x)/x

x²+10=7x

x²-7x+10=0

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-7x+10=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-7~e~c=10\\\\\Delta=(b)^{2}-4(a)(c)=(-7)^{2}-4(1)(10)=49-(40)=9\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-7)-\sqrt{9}}{2(1)}=\frac{7-3}{2}=\frac{4}{2}=2\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-7)+\sqrt{9}}{2(1)}=\frac{7+3}{2}=\frac{10}{2}=5\\S=\{2,~5\}$

Para x=2

y=10/x =10/2=5

Para x=5

y=10/x=10/5=2