Ta có : \(Q=-2x^2-6x+5\)
\(\Leftrightarrow Q=-2\left(x^2+3x-\dfrac{5}{2}\right)\)
\(\Leftrightarrow Q=-2\left(x^2+2x.\dfrac{3}{2}+\dfrac{9}{4}-\dfrac{19}{4}\right)\)
\(\Leftrightarrow Q=-2\left[\left(x+\dfrac{3}{2}\right)^2-\dfrac{19}{4}\right]\)
\(\Leftrightarrow Q=-2\left(x+\dfrac{3}{2}\right)^2+\dfrac{19}{2}\le\dfrac{19}{2}\forall x\)
Dấu " = " xảy ra
\(\Leftrightarrow x+\dfrac{3}{2}=0\Leftrightarrow x=-\dfrac{3}{2}\)
Vậy GTNN của Q là : \(\dfrac{19}{2}\Leftrightarrow x=-\dfrac{3}{2}\)
:D
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