Question

$Care~este~minimul~acestei~expresii~: \\ E(x)= \frac{x ^{2}-4x-4 }{ x^{2} -4x+8} \\ Va~rog~foarte~mult~,as~vrea~si~explicatii~,multumesc!$

Answer 1

$E(x)= 1-\frac{12}{(x-2)^2+4} \\ \\~E(x)=minim~ \Leftrightarrow \frac{12}{(x-2)^2+4}=maxim~(cu~cat~scazi~mai~putin,~ \\ \\ cu~atat~rezultatul~este~mai~mare)~(ma~refer~la~o~cantitate \\ \\ pozitiva,~desigur.) \\ \\ \frac{12}{(x-2)^2+4} =maxim \Rightarrow (x-2)^2+4=minim~(cu~cat~imparti~ \\ \\ "mai~putin",~cu~atat~rezultatul~este~mai~mare) \\ \\ (x-2)^2+4 \geq 4 .~Minimul~se~obtine~pentru~x=2. \\ \\ E(2)=-2.$