Question

Tìm GTNN của biểu thức

a, A=x²+x+1

a, B=2x²+3x+5

Answer 1

A=x²+x+1

=(x²+2.\(\frac{1}{2}\)x+\(\frac{1}{4}\))+1-\(\frac{1}{4}\)

=(x+\(\frac{1}{2}\))²\(+\frac{3}{4}\)\(\ge\frac{3}{4}\)

Để A=\(\frac{3}{4}\) thì : \(\Leftrightarrow\left(x+\frac{1}{2}\right)^2=0\)

\(\Leftrightarrow\)x=\(\frac{1}{2}\)

vạy Min A=\(\frac{3}{4}\Leftrightarrow x=\frac{1}{2}\)

B=2x²+3x+5

=2(x²+\(\frac{3}{2}x\))+5

=2(x²+2.\(\frac{3}{4}x+\frac{9}{16}\))+5-2.\(\frac{9}{16}\)

=2(x+\(\frac{3}{4}\))²+\(\frac{53}{16}\)\(\ge\frac{53}{16}\)

Để B=\(\frac{53}{16}thì:\Leftrightarrow\left(x+\frac{3}{4}\right)^2=0\)

\(\Leftrightarrow x=-\frac{3}{4}\)

Vậy Min B= \(\frac{53}{16}\Leftrightarrow x=-\frac{3}{4}\)