Question

Tìm Min A = 5 - x² / x² - 7

Answer 1

\(A=\frac{-\left(x^2-7\right)-2}{x^2-7}=-1-\frac{2}{x^2-7}\)

Ta có

\(x^2\ge0\) với mọi x

\(\Rightarrow x^2-7\ge-7\)

\(\Rightarrow\frac{1}{x^2-7}\le-\frac{1}{7}\)

\(\Rightarrow-\frac{2}{x^2-7}\ge\frac{2}{7}\)

\(\Rightarrow5-\frac{2}{x^2-7}\ge\frac{37}{7}\)

\(\Rightarrow A\ge\frac{37}{7}\)

Dấu "  =  " xảy ra khi x=0

Vậy Min_A=\(\frac{37}{7}\) khi x=o