Question

tìm Amin Amax nếu có biết A=5-x/x-2 (x thuoc Z)

Answer 1

\(A=\frac{5-x}{x-2}\)

\(\Leftrightarrow-A=\frac{x-5}{x-2}\)

\(\Leftrightarrow-A=\frac{x-2-3}{x-2}=1-\frac{3}{x-2}\)

Xét \(x>2\Leftrightarrow\frac{3}{x-2}>0\)

      \(x< 2\Leftrightarrow\frac{3}{x-2}< 0\)

Suy ra -A đạt GTNN\(\Leftrightarrow x>2\)

Mà \(x\inℤ\)nên x = 3 

\(\Rightarrow-A_{min}=\frac{2}{1}=2\)

hay \(A_{max}=-2\Leftrightarrow x=3\)