Question

Tìm GTLN

-x² + 3x

Answer 1

\(-x^2+3x=-\left(x^2-3x+\dfrac{9}{4}\right)+\dfrac{9}{4}=-\left(x-\dfrac{3}{2}\right)^2+\dfrac{9}{4}\le\dfrac{9}{4}\)

\(ĐTXR\Leftrightarrow x=\dfrac{3}{2}\)

Answer 2

\(=-\left(x^2-2\cdot\dfrac{3}{2}x+\dfrac{9}{4}\right)+\dfrac{9}{4}=-\left(x-\dfrac{3}{2}\right)^2+\dfrac{9}{4}\le\dfrac{9}{4}\)

Dấu \("="\Leftrightarrow x=\dfrac{3}{2}\)