Question

Tìm gtln,gtnn

A=2x^2+6x

Answer 1

\(A=2x^2+6x\\ =2\left(x+\dfrac{3}{2}\right)^2-\dfrac{9}{2}\)

Với mọi x;y thì \(2\left(x+\dfrac{3}{2}\right)^2\ge0\\ \Rightarrow2\left(x+\dfrac{3}{2}\right)^2-\dfrac{9}{2}\ge-\dfrac{9}{2}\)

Hay \(A\ge-\dfrac{9}{2}\)

Để \(A=\dfrac{9}{2}\) thì \(\left(x+\dfrac{3}{2}\right)^2=0\)

=>\(x+\dfrac{3}{2}=0\)

=>\(x=-\dfrac{3}{2}\)

Vậy...