\(f\left(x\right)=-x^2-5x-10=-\left(x^2+5x+10\right)\)
\(=-\left[x^2+5x+\dfrac{40}{4}\right]=-\left[x^2+5x+\dfrac{25}{4}+\dfrac{15}{4}\right]\)
\(=-\left[\left(x+\dfrac{5}{2}\right)^2+\dfrac{15}{4}\right]=-\left(x+\dfrac{5}{2}\right)^2-\dfrac{15}{4}\)
Ta thấy: \(-\left(x+\dfrac{5}{2}\right)^2\le0\forall x\)
\(\Rightarrow-\left(x+\dfrac{5}{2}\right)^2-\dfrac{15}{4}< 0\forall x\)
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