Question

Giúp mình với

Tìm GTLN của:

A = 7 - x - x²
 

Answer 1

\(A=-\left(x^2+x+\dfrac{1}{4}\right)+\dfrac{29}{4}=-\left(x+\dfrac{1}{2}\right)^2+\dfrac{29}{4}\le\dfrac{29}{4}\\ A_{max}=\dfrac{29}{4}\Leftrightarrow x=-\dfrac{1}{2}\)

Answer 2

\(A=-\left(x^2-x+\dfrac{1}{4}\right)+\dfrac{29}{4}=-\left(x-\dfrac{1}{2}\right)^2+\dfrac{29}{4}\le\dfrac{29}{4}\)

Dấu "=" xảy ra \(\Leftrightarrow x=\dfrac{1}{2}\)

Vậy \(A_{max}=\dfrac{29}{4}\Leftrightarrow x=\dfrac{1}{2}\)