Question

Resolva: logx (x²-6)=1

Answer 1

$log_{x} (x^2 - 6) = 1\\ x^{1} = x^2 - 6\\ x^2 - x - 6 = 0\\ \\ \Delta = b^2 - 4.a.c\\ \Delta = (-1)^2 - 4.(1).(-6)\\ \Delta = 1 + 24\\ \Delta = 25$
$x = \frac{-b \pm \sqrt{\Delta}}{2a}\\ \\ x = \frac{1 \pm 5}{2}\\ \\ x' = 3 \\ x'' = -2\\ \\ Condi \c{c}\~ao \ de \ exist\^encia:\\ \\ x \ \textgreater \ 0\\ x \neq 1\\ \\ x^2 - 6\ \textgreater \ 0\\ x \ \textgreater \ \pm \sqrt{6}\\ \\ Solu\c{c}\~ao: S = \{x \in R/ x = 3\}$