Question

tìm giá trị lớn nhất của 

-5x-x^2-20

giúp em mai phải nộp rùi!!!

 

Answer 1

\(-5x-x^2-20\)

\(\Rightarrow-x^2-5x-20\)

\(\Rightarrow-\left(x^2+5x+20\right)\)

\(\Rightarrow-\left(x^2+2.x.\frac{5}{2}+\frac{25}{4}+\frac{55}{4}\right)\)

\(\Rightarrow-\left(x^2+2.x.\frac{5}{2}+\frac{25}{4}\right)-\frac{55}{4}\)

\(\Rightarrow-\left(x+\frac{5}{2}\right)^2-\frac{55}{4}\)

Ta có \(-\left(x+\frac{5}{2}\right)^2\le0\)

\(\Rightarrow-\left(x+\frac{5}{2}\right)^2-\frac{55}{4}\le-\frac{55}{4}\)

Vậy \(-5x-x^2-20\) có GTLN là \(-\frac{55}{4}\)

Khi \(\left(x+\frac{5}{2}\right)^2=0\)\(\Rightarrow x+\frac{5}{2}=0\)\(\Rightarrow x=-\frac{5}{2}\)