Question

Tìm GTLN của biểu thức:

\(A=-x+5\sqrt{x}\)

Answer 1

\(A=-x+5\sqrt{x}\)

\(=-x+5\sqrt{x}-\dfrac{25}{4}+\dfrac{25}{4}\)

\(=-\left(x-5\sqrt{x}+\dfrac{25}{4}-\dfrac{25}{4}\right)\)

\(=-\left[\left(x-5\sqrt{x}+\dfrac{25}{4}\right)-\dfrac{25}{4}\right]\)

\(=-\left[\left(\sqrt{x}-\dfrac{5}{2}\right)^2-\dfrac{25}{4}\right]\le\dfrac{25}{4}\)

Vậy \(\)\(MAX_A=\dfrac{25}{4}\) khi \(\left(\sqrt{x}-\dfrac{5}{2}\right)^2=0\Leftrightarrow x=\dfrac{25}{4}\)

Answer 2

GTLN là 5 khi x = - 5