Question

tìm gtln

a,\(A=-x^2-4x+9\)

b,\(B=-3x-2x^2-5\)

c,\(C=4-x^2+2xy-2y^2-6y\)

Answer 1

a) ta có : \(A=-x^2-4x+9=-\left(x^2+4x+4\right)+13\)

\(=-\left(x+2\right)^2+13\le13\) \(\Rightarrow A_{max}=13\) khi \(x=-2\)

b) ta có : \(B=-3x-2x^2-5=-2\left(x^2+\dfrac{3}{2}x+\dfrac{9}{16}\right)-\dfrac{31}{8}\)

\(=-2\left(x+\dfrac{3}{4}\right)^2-\dfrac{31}{8}\le\dfrac{-31}{8}\) \(\Rightarrow B_{max}=-\dfrac{31}{8}\) khi \(x=\dfrac{-3}{4}\)

c) ta có : \(C=4-x^2+2xy-2y^2-6y=-x^2+2xy-y^2-y^2-6y-9+13\)

\(=-\left(x-y\right)^2-\left(y+3\right)^2+13\le13\) \(\Rightarrow C_{max}=13\) khi \(x=y=-3\)