Question

giup minh bai toan nay

2x-2x^2-5(tim gia tri lon nhat)

Answer 1

\(2x-2x^2-5\)

=\(-2\left(x^2-x+\dfrac{5}{2}\right)\)

=\(-2\left(x^2-x+\dfrac{1}{4}+\dfrac{9}{4}\right)\)

\(=-2\left(x-\dfrac{1}{2}\right)^2-\dfrac{9}{2}\)

Với mọi x thì \(-\left(x-\dfrac{1}{2}\right)-\dfrac{9}{2}>=-\dfrac{9}{2}\)

Để \(-2\left(x-\dfrac{1}{2}\right)-\dfrac{9}{2}=-\dfrac{9}{2}\)thì

\(\left(x-\dfrac{1}{2}\right)^2=0\)=>\(x-\dfrac{1}{2}=0\)=>\(x=\dfrac{1}{2}\)

Vậy ...