\(B=\sqrt[3]{170-78\sqrt{3}}+\sqrt[3]{170+78\sqrt{3}}\)
\(\Rightarrow B^3=\left(\sqrt[3]{170-78\sqrt{3}}+\sqrt[3]{170+78\sqrt{3}}\right)^3\)
\(=170-78\sqrt{3}+170+78\sqrt{3}+3\sqrt[3]{170-78\sqrt{3}}.\sqrt[3]{170+78\sqrt{3}}\left(\sqrt[3]{170-78\sqrt{3}}+\sqrt[3]{170+78\sqrt{3}}\right)\)
\(=340+3B\sqrt[3]{\left(170-78\sqrt{3}\right)\left(170+78\sqrt{3}\right)}\)
\(=340+3B\sqrt[3]{28900-18252}\)
\(=340+3B\sqrt[3]{10648}\)
\(=340+3B.22\)
\(=340+66B\)
\(\Rightarrow B^3-66B-340=0\)
\(\Leftrightarrow\left(B-10\right)\left(B^2+10B+34\right)=0\)
\(\Leftrightarrow B-10=0\) (vì \(B^2+10B+34=\left(B^2+10B+25\right)+9=\left(B+5\right)^2+9>0\))
\(\Leftrightarrow B=10\)
Vậy \(B=10\)
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