1) Ta có:
\(P\left(x\right)=x^2-2\left(2x-3\right)\)
\(P\left(x\right)=x^2-4x+6\)
\(P\left(x\right)=x^2-2.x.2+4+2\)
\(P\left(x\right)=\left(x-2\right)^2+2\)
Vì \(\left(x-2\right)^2\ge0\) với mọi x
\(\Rightarrow\left(x-2\right)^2+2\ge2\) với mọi x
\(\Rightarrow P\left(x\right)min=2\Leftrightarrow x=2\)
2) Ta có:
\(Q\left(x\right)=-4x^2+4x+3\)
\(Q\left(x\right)=-\left(2x\right)^2+2.2x-1+4\)
\(Q\left(x\right)=-\left[\left(2x\right)^2-2.2x+1\right]+4\)
\(Q\left(x\right)=-\left(2x-1\right)^2+4\)
Vì \(-\left(2x-1\right)^2\le0\) với mọi x
\(\Rightarrow-\left(2x-1\right)^2+4\le4\) với mọi x
\(\Rightarrow Q\left(x\right)max=4\Leftrightarrow x=\dfrac{1}{2}\)
