Question

[Trang Nguyễn]

Tìm GTLN hoặc GTLN:

a) `A = (5x^2 - 24x + 32)/(x^2 - 4x + 4)`

b) `B = ( 10x^2 + 24x + 15)/(x^2 + 2x + 1)`

Answer 1

[Nguyễn Việt Lâm]

\(A=\dfrac{4\left(x^2-4x+4\right)+\left(x^2-8x+16\right)}{x^2-4x+4}=4+\left(\dfrac{x-4}{x-2}\right)^2\ge4\)

\(A_{min}=4\) khi \(x=4\) (A max ko tồn tại)

\(B=\dfrac{6\left(x^2+2x+1\right)+\left(4x^2+12x+9\right)}{x^2+2x+1}=6+\left(\dfrac{2x+3}{x+1}\right)^2\ge6\)

\(B_{min}=6\) khi \(x=-\dfrac{3}{2}\) 

B max ko tồn tại