\(B=-5x^2-4x+1\)
\(=\frac{9}{5}-5x^2-4x-\frac{4}{5}\)
\(=\frac{9}{5}-5\left(x^2+\frac{4x}{5}+\frac{4}{25}\right)\)
\(=\frac{9}{5}-5\left(x+\frac{2}{5}\right)^2\le\frac{9}{5}\)
Đẳng thức xảy ra khi \(x=-\frac{2}{5}\)
\(C=\frac{2}{6x-5-9x^2}\)
Ta có:
\(6x-5-x^2=-9x^2+6x-1-5\)
\(=-9\left(x^2-\frac{2x}{3}+\frac{1}{9}\right)-4\)
\(=-9\left(x-\frac{1}{3}\right)^2-4\le-4\)
\(\Rightarrow\frac{1}{-9\left(x-\frac{1}{3}\right)^2-4}\ge-\frac{1}{4}\)
\(\Rightarrow\frac{2}{-9\left(x-\frac{1}{3}\right)^2-4}\ge-\frac{2}{4}=-\frac{1}{2}\)
Đẳng thức xảy ra khi \(x=\frac{1}{3}\)
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