Question

{X2+y2=20
{X+y=6
Quero isolar o X aguem pode fazer esta conta para mim ??

Answer 1

Resposta:

x=2 e y=4

ou

x=4 e y=2

Explicação passo-a-passo:

x²+y²=20

x+y=6

x+y=6 => y=6-x

x²+y²=20 => x²+(6-x)²=20 =>x²+36-12x+x²=20 => 2x²-12x+16=0 => ÷2 =>

x²-6x+8=0

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-6x+8=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-6~e~c=8\\\\\Delta=(b)^{2}-4(a)(c)=(-6)^{2}-4(1)(8)=36-(32)=4\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-6)-\sqrt{4}}{2(1)}=\frac{6-2}{2}=\frac{4}{2}=2\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-6)+\sqrt{4}}{2(1)}=\frac{6+2}{2}=\frac{8}{2}=4$

Para x=2

y=6-x=6-2=4

Para x=4

y=6-x=6-4=2