+Tim GTNN cua A:
\(A=\frac{3-4x}{x^2+1}\)
Xet : 3-4x=x^2-4x+4-x^2-1=(x-2)^2-(x^2+1)
\(\Rightarrow\frac{\left(x-2\right)^2-\left(x^2+1\right)}{x^2+1}=\frac{\left(x-2\right)^2}{x^2+1}-\frac{x^2+1}{x^2+1}=\frac{\left(x-2\right)^2}{x^2+1}-1\)
Ma: \(\frac{\left(x-2\right)^2}{x^2+1}\ge0\)
\(\Rightarrow\frac{\left(x-2\right)^2}{x^2+1}-1\ge-1\)
Vay MinA=-1 va x=2
+ Tim GTLN cua A:
\(A=\frac{3-4x}{x^2+1}\)
Xet : 3-4x=4x^2+4-4x^2-4x-1=(4x^2+4)-(4x^2+4x+1)=4(x^2+1)-(2x+1)^2
\(\Rightarrow\frac{4\left(x^2+1\right)-\left(2x+1\right)^2}{x^2+1}=\frac{4\left(x^2+1\right)}{x^2+1}-\frac{\left(2x+1\right)^2}{x^2+1}=4-\frac{\left(2x+1\right)^2}{x^2+1}\)
Ma : \(\frac{\left(2x+1\right)^2}{x^2+1}\ge0\Rightarrow4-\frac{\left(2x+1\right)^2}{x^2+1}\le4\)
Vay MaxA=4 va x=-1/2
k nhe
