Question

Ai giúp tôi với

tìm giá trị nhỏ nhất của C = x^6+27 / x^4-3x^3+6x^2-9x+9

Answer 1

C=\(\dfrac{x^6+27}{x^4-3x^3+6x^2-9x+9}=\dfrac{\left(x^2+3\right)\left(x^4-3x^2+9\right)}{\left(x^4+3x^2\right)-\left(3x^3+9x\right)+\left(3x^2+9\right)}=\dfrac{\left(x^2+3\right)\left(x^4+6x^2+9-9x^2\right)}{\left(x^2+3x\right)\left(x^2-3x+3\right)}=\dfrac{\left(x^2+3+3x\right)\left(x^2+3-3x\right)}{x^2+3-3x}=x^2+3x+3=\left(x^2+3x+\dfrac{9}{4}\right)-\dfrac{9}{4}+3=\left(x+\dfrac{3}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\) Dấu "=" xảy ra \(\Leftrightarrow\left(x+\dfrac{3}{2}\right)^2=0\Leftrightarrow x=\dfrac{-3}{2}\)

Vậy Min C bằng \(\dfrac{3}{4}\Leftrightarrow x=\dfrac{-3}{2}\)

Answer 2

Min C=\(\dfrac{3}{4}\Leftrightarrow x=\dfrac{-3}{2}\)