b) Ta có: \(P=\sqrt{\dfrac{14+3\sqrt{3}}{2}}+\sqrt{\dfrac{16+2\sqrt{15}}{3}}-\dfrac{11\sqrt{3}}{6}\)
\(=\sqrt{\dfrac{28+6\sqrt{3}}{4}}+\sqrt{\dfrac{16+2\sqrt{15}}{3}}-\dfrac{11\sqrt{3}}{6}\)
\(=\dfrac{3\sqrt{3}+1}{2}+\dfrac{\sqrt{15}+1}{\sqrt{3}}-\dfrac{11\sqrt{3}}{6}\)
\(=\dfrac{3\sqrt{3}+1}{2}+\dfrac{3\sqrt{5}+\sqrt{3}}{3}-\dfrac{11\sqrt{3}}{6}\)
\(=\dfrac{3\left(3\sqrt{3}+1\right)+2\left(3\sqrt{5}+\sqrt{3}\right)-11\sqrt{3}}{6}\)
\(=\dfrac{9\sqrt{3}+9+6\sqrt{5}+2\sqrt{3}-11\sqrt{3}}{6}\)
\(=\dfrac{9+6\sqrt{5}}{6}\)
\(=\dfrac{3+2\sqrt{5}}{2}\)
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