\(P=\dfrac{\sqrt{c-4}}{c}+\dfrac{\sqrt{a-2}}{a}+\dfrac{\sqrt{b-3}}{b}=\dfrac{2.2.\sqrt{c-4}}{4c}+\dfrac{2.\sqrt{2}.\sqrt{a-2}}{2\sqrt{2}a}+\dfrac{2.\sqrt{3}.\sqrt{b-3}}{2\sqrt{3}b}\)
\(P\le\dfrac{4+c-4}{4c}+\dfrac{2+a-2}{2\sqrt{2}a}+\dfrac{3+b-3}{2\sqrt{3}b}=\dfrac{1}{4}+\dfrac{1}{2\sqrt{2}}+\dfrac{1}{2\sqrt{3}}\)
\(P_{max}=\dfrac{1}{4}+\dfrac{1}{2\sqrt{2}}+\dfrac{1}{2\sqrt{3}}\) khi \(\left(a;b;c\right)=\left(4;6;8\right)\)
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