Question

Dada a função f(x)=x²-6x+8, determine x, se houver, para que se tenha :
a) f(x)=3

Answer 1

$f(x)~=~x^2-6x+8\\\\\\\\Para~f(x)~=~3:\\\\\\3~=~x^2-6x+8\\\\\\\boxed{x^2-6x+5~=~0}\\\\\\\\\Delta~=~(-6)^2-4.1.5\\\\\\\Delta~=~36-20\\\\\\\boxed{\Delta~=~16}\\\\\\\\x'~=~\frac{6+\sqrt{16}}{2~.~1}\\\\\\x'~=~\frac{6+4}{2}\\\\\\\boxed{x'~=~5}\\\\\\\\x''~=~\frac{6-\sqrt{16}}{2~.~2}\\\\\\x''~=~\frac{6-4}{2}\\\\\\\boxed{x''~=~1}$