`@`\(A=x^2-6x+11\)
\(A=x^2-6x+9+2\)
\(A=\left(x-3\right)^2+2\ge2\)
Dấu "=" xảy ra khi `x=3`
`@`\(B=2x^2+10x-1\)
\(B=2\left(x^2+5x\right)-1\)
\(B=2\left(x^2+5x+\dfrac{25}{4}\right)-\dfrac{25}{8}-1\)
\(B=2\left(x+\dfrac{5}{2}\right)^2-\dfrac{33}{8}\ge-\dfrac{33}{8}\)
Dấu "=" xảy ra khi `x=-5/2`
`@`\(C=5x-5x^2\)
\(C=-5\left(x^2-x\right)\)
\(C=-5\left(x^2-x+\dfrac{1}{4}\right)+\dfrac{5}{4}\)
\(C=-5\left(x-\dfrac{1}{2}\right)^2+\dfrac{5}{4}\le\dfrac{5}{4}\)
Dấu "=" xảy ra khi `x=1/2`
\(A=\left(x^2-6x+9\right)+2=\left(x-3\right)^2+2\)
Do \(\left(x-3\right)^2\ge0;\forall x\Rightarrow A\ge2\)
\(A_{min}=2\) khi \(x=3\)
\(B=2\left(x^2+5x+\dfrac{25}{4}\right)-\dfrac{27}{2}=2\left(x+\dfrac{5}{2}\right)^2-\dfrac{27}{2}\ge-\dfrac{27}{2}\)
\(B_{min}=-\dfrac{27}{2}\) khi \(x=-\dfrac{5}{2}\)
\(C=-5\left(x^2-x+\dfrac{1}{4}\right)+\dfrac{5}{4}=-5\left(x-\dfrac{1}{2}\right)^2+\dfrac{5}{4}\le\dfrac{5}{4}\)
\(C_{max}=\dfrac{5}{4}\) khi \(x=\dfrac{1}{2}\)
