Question

Найдите нули функции Y=|x^2+4|x|-5|

Answer 1

$y=|x^2+4|x|-5|\\\\y=0\ \ ,\ \ \ |\, x^2+4|x|-5\, |=0\ \ \Rightarrow \ \ \ x^2+4|x|-5=0\ \ ,\\\\x^2=|x|^2\ \ \to \ \ |x|^2+4|x|-5=0\ \ \ \Rightarrow \ \ \ \ a)\ |x|=-5\ \ ,\ \ b)\ |x|=1\ \ (teor.\ Vieta)\\\\a)\ \ |x|=-5\ \ \to \ \ x\in \varnothing\ ,\ tak\ kak\ \ \ |x|\geq 0\\\\b)\ \ |x|=1\ \ \Rightarrow \ \ \ x=\pm 1\\\\Otvet:\ \ x=-1\ ,\ x=1\ .$