Question

Tìm GTNN của \(K=\dfrac{2}{6x-5-9x^2}\)

Answer 1

Ta thấy: \(6x-5-9x^2\)

\(=-9x^2+6x-1-4\)

\(=-9\left(x^2-\dfrac{2x}{3}+\dfrac{1}{9}\right)-4\)

\(=-9\left(x-\dfrac{1}{3}\right)^2-4\le-4\forall x\)

\(\Rightarrow\dfrac{1}{-9\left(x-\dfrac{1}{3}\right)^2-4}\ge\dfrac{1}{4}\forall x\)

\(\Rightarrow K=\dfrac{2}{-9\left(x-\dfrac{1}{3}\right)^2-4}\ge\dfrac{2}{4}=\dfrac{1}{2}\forall x\)

Đẳng thức xảy ra khi \(-9\left(x-\dfrac{1}{3}\right)^2=0\Rightarrow x=-\dfrac{1}{3}\)