Question

Encontre o valor de T na equação x(ao quadrado) - 12x + T = 0 , sabendo que x um = x dois + 6 e que x um e x dois são raízes dessa equação

Answer 1

Podemos utilizar as relações de soma e produto das raízes, veja:

$\boxed{x'~+~x''~=~-\frac{b}{a}}\\\\\\x'~+~x''~=~-\frac{(-12)}{1}\\\\\\Substituindo~o~valor~de~x':\\\\\\(x''+6)~+~x''~=~12\\\\\\2x''~=~12-6\\\\\\x''~=~\frac{6}{2}\\\\\\\boxed{x''~=~3}\\\\\\Com~o~valor~de~x''~podemos~determinar~x':\\\\\\x'~=~x''+6\\\\\\x'~=~3+6\\\\\\\boxed{x'~=~9}\\\\\\\\\boxed{x'~.~x''~=~\frac{c}{a}}\\\\\\9~.~3~=~\frac{T}{1}\\\\\\\boxed{T~=~27}$