Question

cho B = \(\dfrac{\left(x^2-5x+6\right)\left(x^2-5x+4\right)}{\left(x-4\right)\left(x-3\right)}\)

Tìm giá trị nhỏ nhất của B

Answer 1

\(B=\dfrac{\left(x-2\right)\left(x-3\right)\left(x-1\right)\left(x-4\right)}{\left(x-4\right)\left(x-3\right)}=\left(x-2\right)\left(x-1\right)\)

\(B=x^2-3x+2=\left(x-\dfrac{3}{2}\right)^2-\dfrac{1}{4}\ge-\dfrac{1}{4}\)

\(B_{min}=-\dfrac{1}{4}\) khi \(x=\dfrac{3}{2}\)

Answer 2

\(B=\dfrac{\left(x-3\right)\left(x-2\right)\left(x-4\right)\left(x-1\right)}{\left(x-4\right)\left(x-3\right)}=\left(x-2\right)\left(x-1\right)=x^2-3x+2=\left(x-\dfrac{3}{2}\right)^2-\dfrac{1}{4}\ge-\dfrac{1}{4}\)

với mọi x.

\(B_{min}=-\dfrac{1}{4}\) tại \(x=\dfrac{3}{2}\)