Question

Tìm GTNN của \(A=x-2\sqrt{x+2}\)

Answer 1

\(A=x-2\sqrt{x+2}=x+2-2\sqrt{x+2}+1-3=\left(\sqrt{x+2}-1\right)^2-3\ge-3\)

Dấu "=" xảy ra khi \(\sqrt{x+2}-1=0\Leftrightarrow\sqrt{x+2}=1\Leftrightarrow x+2=1\Leftrightarrow x=-1\)

Vậy \(Min_A=-3\) khi x=-1

Answer 2

≥-2)

2√(x+2)+1-3

A=\(\left(\sqrt{x+2}-1\right)^2-3\)

Ta có (\(\left(\sqrt{x+2}-1\right)^2\)≥0

<=>\(\left(\sqrt{x+2}-1\right)^2-3\)≥-3

<=> A≥3

Dấu = xảy ra<=>\(\left(\sqrt{x+2}-1\right)^2\)=0

<=> \(\sqrt{x+2}\)-1=0

<=>\(\sqrt{x+2}\)=1

<=> x+2=1

<=> x=-1 (tm)

Vậy GTNN A=-3 khi x=-1