\(M=4x-x^2+3\)
\(=-\left(x^2-4x\right)+3\)
\(=-\left(x^2-4x+4\right)+7\)
\(=-\left(x-2\right)^2+7\)
\(-\left(x-2\right)^2\le0\forall x\)
\(\Rightarrow M=-\left(x-2\right)^2+7\le7\forall x\)
Dấu "=" xảy ra khi x-2=0 ⇔ x = 2
Vậy: ...
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\(N=x-x^2\)
\(=-\left(x^2-x\right)=-\left(x^2-x+\dfrac{1}{4}\right)+\dfrac{1}{4}\)
\(=-\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{4}\)
\(-\left(x-\dfrac{1}{2}\right)^2\le0\forall x\)
\(\Rightarrow N=-\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{4}\le\dfrac{1}{4}\forall x\)
Dấu "=" xảy ra: `x-1/2=0⇔x=1/2`
Vậy: ...
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\(P=2x-2x^2-5\)
\(=-2\left(x^2-x\right)-5=-2\left(x^2-x+\dfrac{1}{4}\right)-\dfrac{9}{2}\)
\(=-2\left(x-\dfrac{1}{2}\right)^2-\dfrac{9}{2}\)
\(-2\left(x-\dfrac{1}{2}\right)^2\le0\forall x\)
\(\Rightarrow P=-2\left(x-\dfrac{1}{2}\right)^2-\dfrac{9}{2}\le-\dfrac{9}{2}\forall x\)
Dấu "=" xảy ra: `x-1/2=0⇔x=1/2`
Vậy: ...
