Question

BT: tìm gtnn :

a) \(A=\frac{x^2-2x-2}{x^2+x+1}\)

b) \(A=\frac{8x+3}{4x^2+1}\)

c) \(A=\frac{27-2x}{x^2+9}\)

Answer 1

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

Ta có:\(\frac{3x^2}{x^2+x+1}\ge0\Rightarrow\frac{3x^2}{x^2+x+1}-2\ge-2\)

=>Min A=-2 <=>3x²=0<=>x=0

 

Answer 2

\(\frac{27-12x}{x^2+9}=\frac{\left(x^2-12x+36\right)-\left(x^2+9\right)}{x^2+9}=\frac{\left(x-6\right)^2}{x^2+9}-1\)

ta thấy (x-6)² >= 0 vs mọi x

          x² + 9 >0

=> (x-6)² / x² +9 -1 >= -1