Question

[Vu Ngoc Thuy Linh_2003]

Tim gia tri nho nhat cua cac bieu thuc sau:

B=2x²+10x-1

C=5x-x²

Answer 1

[o0o I am a studious person o0o]

\(2x^2+10x-1\)

\(=2\left(x^2+5x-\frac{1}{2}\right)\)

\(=2\left(x^2+2.x.\frac{5}{2}+\frac{25}{4}-\frac{27}{4}\right)\)

\(=2\left(\left(x+\frac{5}{2}\right)^2-\frac{27}{4}\right)\)

\(=\frac{-27}{2}-2\left(x+\frac{5}{2}\right)^2\le\frac{-27}{2}\)

\(MinB=\frac{-27}{2}\Leftrightarrow x+\frac{5}{2}=0\Rightarrow x=-\frac{5}{2}\)

Answer 2

[Minh Ánh]

Min B= -1 khi x=0

Min C=0 khi x=0