Question

a) Tìm min A biết \(A=\dfrac{2x^2-16x+41}{x^2-8x+22}\)

b) Tìm min B biết \(B=\dfrac{x^2-4x+1}{x^2}\)

c) Tìm min C biết \(C=\dfrac{4x^2-6x+3}{\left(2x-1\right)^2}\)

d) Tìm max D biết \(D=\dfrac{x^2}{x^4+1}\)

Answer 1

a)

\(A=\dfrac{2x^2-16x+41}{x^2-8x+22}=\dfrac{2\left(x^2-8x+22\right)-3}{x^2-8x+22}\)

\(A-2=-\dfrac{3}{x^2-8x+22}=-\dfrac{3}{\left(x-4\right)^2+6}\ge-\dfrac{3}{6}=-\dfrac{1}{2}\)

\(A\ge\dfrac{3}{2}\) khi x =4