Question

{x+y=9
{x²+y²-2x-2y=23​

Answer 1

Resposta:

x=4 e y=5 ou

x=5 e y=4

Explicação passo-a-passo:

x+y=9

x²+y²-2x-2y=23​ => x²+y²-2(x+y)=23 =>  x²+y²-2.9=23 => x²+y²-18=23 => x²+y²=23+18 => x²+y²=41

x+y=9  => y=9-x

Substituindo y=9-x em x²+y²=41

x²+(9-x)²=41

x²+81-18x+x²=41

2x²-18x+40=0 (÷2)

x²-9x+20=0

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-9x+20=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-9~e~c=20\\\\\Delta=(b)^{2}-4(a)(c)=(-9)^{2}-4(1)(20)=81-(80)=1\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-9)-\sqrt{1}}{2(1)}=\frac{9-1}{2}=\frac{8}{2}=4\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-9)+\sqrt{1}}{2(1)}=\frac{9+1}{2}=\frac{10}{2}=5\\\\S=\{4,~5\}$

Para x=4

y=9-x=9-4=5

Para x=5

y=9-x=9-5=4