a)
\(P=5x-x^2\\ =-\left(x^2-5x\right)=-\left(x^2-2.x.\dfrac{5}{2}+\dfrac{25}{4}-\dfrac{25}{4}\right)\\ =-\left(x-\dfrac{5}{2}\right)^2+\dfrac{25}{4}\le\dfrac{25}{4}\)
b)
\(Q=x^2+2xy+y^2-3y^2+4y+9\\ =\left(x+y\right)^2-3\left(y^2-\dfrac{4}{3}y-9\right)\\ =\left(x+y\right)^2-3\left(y^2-2.y.\dfrac{2}{3}+\dfrac{4}{9}-\dfrac{85}{9}\right)\\ =\left(x+y\right)^2-3\left(\left(x-\dfrac{2}{3}\right)^2-\dfrac{85}{9}\right)\\ =\left(x+y\right)^2-3\left(x-\dfrac{2}{3}\right)^2+\dfrac{85}{9}\le\dfrac{85}{9}\)
Đúng 0
Bình luận (0)
