a, \(A=-x^2+2x+2\)
\(=-\left(x^2-2x-2\right)=-\left(x^2-2x+1-3\right)\)
\(=-\left(x-1\right)^2+3\le3\)
Dấu " = " khi \(-\left(x-1\right)^2=0\Leftrightarrow x=1\)
Vậy \(MAX_A=3\) khi x = 1
b, \(B=-x^2-8x+17\)
\(=-\left(x^2+8x-17\right)\)
\(=-\left(x^2+8x+16-33\right)\)
\(=-\left(x+4\right)^2+33\le33\)
Dấu " = " khi \(-\left(x+4\right)^4=0\Leftrightarrow x=-4\)
Vậy \(MAX_B=33\) khi x = -4
c, \(C=-x^2+7x+15\)
\(=-\left(x^2-\dfrac{7}{2}x.2+\dfrac{49}{4}-\dfrac{109}{4}\right)\)
\(=-\left(x-\dfrac{7}{2}\right)^2+\dfrac{109}{4}\le\dfrac{109}{4}\)
Dấu " = " khi \(-\left(x-\dfrac{7}{2}\right)^2=0\Leftrightarrow x=\dfrac{7}{2}\)
Vậy \(MAX_C=\dfrac{109}{4}\) khi \(x=\dfrac{7}{2}\)
d, \(D=-x^2-5x+11\)
\(=-\left(x^2+\dfrac{5}{2}.x.2+\dfrac{25}{4}-\dfrac{69}{4}\right)\)
\(=-\left(x+\dfrac{5}{2}\right)^2+\dfrac{69}{4}\le\dfrac{69}{4}\)
Dấu " = " khi \(-\left(x+\dfrac{5}{2}\right)^2=0\Leftrightarrow x=\dfrac{-5}{2}\)
Vậy \(MAX_D=\dfrac{69}{4}\) khi \(x=\dfrac{-5}{2}\)
f, sai đề à?
g, \(G=-x^2-x-y^2-3y+13\)
\(=-\left(x^2+x+y^2+3y-13\right)\)
\(=-\left(x^2+\dfrac{1}{2}x.2.+\dfrac{1}{4}+y^2+\dfrac{3}{2}.x.2+\dfrac{9}{4}-15,5\right)\)
\(=-\left(x+\dfrac{1}{2}\right)^2-\left(y+\dfrac{3}{2}\right)^2+15,5\le15,5\)
Dấu " = " khi \(\left\{{}\begin{matrix}-\left(x+\dfrac{1}{2}\right)^2=0\\-\left(y+\dfrac{3}{2}\right)^2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-1}{2}\\y=\dfrac{-3}{2}\end{matrix}\right.\)
Vậy \(MAX_G=15,5\) khi \(\left\{{}\begin{matrix}x=\dfrac{-1}{2}\\y=\dfrac{-3}{2}\end{matrix}\right.\)
