7, \(G=-4x^2+12x-7\)
\(=-4\left(x^2-3x+\dfrac{7}{4}\right)\)
\(=-4\left(x^2-\dfrac{3}{2}.x.2+\dfrac{9}{4}-\dfrac{2}{4}\right)\)
\(=-4\left(x-\dfrac{3}{2}\right)^2+2\le2\)
Dấu " = " khi \(-4\left(x-\dfrac{3}{2}\right)^2=0\Leftrightarrow x=\dfrac{3}{2}\)
Vậy \(MAX_G=2\) khi \(x=\dfrac{3}{2}\)
8, \(H=-2x^2+4x-15\)
\(=-2\left(x^2-2x+\dfrac{15}{2}\right)\)
\(=-2\left(x^2-2x+1+\dfrac{13}{2}\right)\)
\(=-2\left(x-1\right)^2-13\le-13\)
Dấu " = " khi \(-2\left(x-1\right)^2=0\Leftrightarrow x=1\)
Vậy \(MAX_H=-13\) khi x = 1
9, \(K=-x^4+2x^2-2\)
\(=-\left(x^2-2x^2+1+1\right)\)
\(=-\left(x^2-1\right)^2-1\le-1\)
Dấu " = " khi \(-\left(x^2-1\right)^2=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
Vậy \(MAX_K=-1\) khi \(x=\pm1\)
10, \(J=-3x^2+15x-9\)
\(=-3\left(x^2-\dfrac{5}{2}.x.2+\dfrac{10}{4}+\dfrac{2}{4}\right)\)
\(=-3\left(x-\dfrac{5}{2}\right)^2-\dfrac{3}{2}\le\dfrac{-3}{2}\)
Dấu " = " khi \(-3\left(x-\dfrac{5}{2}\right)^2=0\Leftrightarrow x=\dfrac{5}{2}\)
Vậy \(MAX_J=\dfrac{-3}{2}\) khi \(x=\dfrac{5}{2}\)
