Summer Clouds moderators
22/07/2017 at 12:01-
We have :
\(x^2-2x+5=x^2-2x+1+4\)
\(=\left(x-1\right)^2+4\ge4\)
\(\Rightarrow H=\dfrac{1}{x^2-2x+5}\le\dfrac{1}{4}\)
\(\Rightarrow Max_H=\dfrac{1}{4}\)
\(\Leftrightarrow\left(x-1\right)^2=0\)
\(\Leftrightarrow x=1\)
Selected by MathYouLike -
¤« 03/04/2018 at 13:33
We have :
x2−2x+5=x2−2x+1+4
=(x−1)2+4≥4
⇒H=1x2−2x+5≤14
⇒MaxH=14
⇔(x−1)2=0
⇔x=1