Question

Tìm GTLN của B

B=(2-x) (x+3)

Answer 1

\(B=\left(2-x\right)\left(x+3\right)\)

\(\Leftrightarrow B=2-x^2+6-3x\)

\(\Leftrightarrow B=-x^2-3x+8\)

\(\Leftrightarrow B=-\left(x^2+3x-8\right)\)

\(\Leftrightarrow B=-\left(x^2+3x+\dfrac{9}{4}-\dfrac{41}{4}\right)\)

\(\Leftrightarrow B=-\left[\left(x+\dfrac{3}{2}\right)^2-\dfrac{41}{4}\right]\)

\(\Leftrightarrow B=-\left(x+\dfrac{3}{2}\right)^2+\dfrac{41}{4}\le\dfrac{41}{4}\forall x\)

Dấu " = " xảy ra

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

Vậy Max B là : \(\dfrac{41}{4}\Leftrightarrow x=-\dfrac{3}{2}\)

:D