Giải:
\(-x^2-2x-2\)
\(=-x^2-2x-1-1\)
\(=-\left(x^2+2x+1\right)-1\)
\(=-\left(x+1\right)^2-1\le-1\)
\(\Leftrightarrow x+1=0\Leftrightarrow x=-1\)
Vậy ...
2) \(-4x^2+12x+10\)
\(=-4x^2+12x-9+19\)
\(=-\left(4x^2-12x+9\right)+19\)
\(=-\left(2x-3\right)^2+19\)
\(=19-\left(2x-3\right)^2\le19\)
\(\Leftrightarrow2x-3=0\Leftrightarrow x=\dfrac{3}{2}\)
Vậy ...
3) \(-x^2-4x\)
\(=-x^2-4x-4+4\)
\(=-\left(x^2+4x+4\right)+4\)
\(=-\left(x+2\right)^2+4\le4\)
\(\Leftrightarrow x+2=0\Leftrightarrow x=-2\)
Vậy ...
4) \(-x^2+6x-5\)
\(=-x^2+6x-9+4\)
\(=-\left(x^2-6x+9\right)+4\)
\(=-\left(x-3\right)^2+4\le4\)
\(\Leftrightarrow x-3=0\Leftrightarrow x=3\)
Vậy ...
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