Question

tim gtnn cua B= 10x^2 -24x+15/ x^2 -2x+1

Answer 1

\(B=\dfrac{10x^2-24x+15}{x^2-2x+1}=\dfrac{10\left(x^2-2x+1\right)-4x+5}{x^2-2x+1}=\dfrac{10\left(x^2-2x+1\right)-4\left(x-1\right)+1}{x^2-2x+1}=10-\dfrac{4}{x-1}+\dfrac{1}{\left(x-1\right)^2}\)

Đặt \(\dfrac{1}{x-1}=t\)

Thay vào B ta được: \(B=10-4t+t^2=\left(t^2-4t+4\right)+6=\left(t-2\right)^2+6\ge6\)

Dấu ''='' xảy ra khi: \(\left(t-2\right)^2=0\) hay \(t=2\)

\(=>\dfrac{1}{x-1}=2=>x-1=\dfrac{1}{2}=>x=\dfrac{3}{2}\)

Vậy với \(x=\dfrac{3}{2}\) thì B đạt GTNN bằng \(6\)