a: \(\sqrt{\left(x-3\right)\left(9-x\right)}\)
\(=\sqrt{9x-x^2-27+3x}\)
\(=\sqrt{-\left(x^2-12x+27\right)}\)
\(=\sqrt{-\left(x^2-12x+36-9\right)}\)
\(=\sqrt{-\left(x-6\right)^2+9}\le3\)
Dấu '=' xảy ra khi x=6
b: \(-x^2+3x+4\)
\(=-\left(x^2-3x-4\right)\)
\(=-\left(x^2-2\cdot x\cdot\dfrac{3}{2}+\dfrac{9}{4}-\dfrac{25}{4}\right)\)
\(=-\left(x-\dfrac{3}{2}\right)^2+\dfrac{25}{4}\le\dfrac{25}{4}\)
Dấu '=' xảy ra khi x=3/2
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