$A^3=10+6\sqrt{3}+10-6\sqrt{3}+3\sqrt[3]{\left(10+6\sqrt{3}\right).\left(10-6\sqrt{3}\right)}A\\
=20+3A\sqrt[3]{10^2-36.3}\\
=20-6A$
$
\Rightarrow A^3+6A-20=0\\
\Rightarrow \left(A-2\right)\left(A^2+2A+10\right)=0$\(\left[ \begin{array}{l}x-2=0\\A^2+2A+10=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}A-2=0\\A^2+2A+10=0(L)\end{array} \right.\) (Do $A^2+2A+10>0$)
⇔\(\left[ \begin{array}{l}A=2\\A^2+2A+10=0(L)\end{array} \right.\)
Vậy A=2
b)
$B^3=26+15\sqrt{3}+26-15\sqrt{3}+3B\sqrt[3]{\left(26+15\sqrt{3}\right).\left(26-15\sqrt{3}\right)}\\
=52+3B\sqrt[3]{26^2-15^2.3}\\
=52+3B$
$\Rightarrow B^3-3B-52=0\\
\Rightarrow \left(x-4\right)\left(x^2+4x+13\right)=0$
⇔\(\left[ \begin{array}{l}B-4=0\\B^2+4B+13=0(L)\end{array} \right.\)
⇔\(\left[ \begin{array}{l}B=4\\B^2+4B+13=0(L)\end{array} \right.\)
Vậy B=4
c) C=$\sqrt[3]{6\sqrt{3}+10}-\sqrt[3]{26+15\sqrt{3}}$
$=\sqrt[3]{\left(\sqrt{3}\right)^3+3\left(\sqrt{3}\right)^2+3\sqrt{3}.1+1^3}-\sqrt[3]{2^3+3.2^2\sqrt{3}+3.2.\left(\sqrt{3}\right)^2+\left(\sqrt{3}\right)^3}$
$=\sqrt[3]{\left(\sqrt{3}+1\right)^3}-\sqrt[3]{\left(2+\sqrt{3}\right)^3}\\
=\sqrt{3}+1-2-\sqrt{3}=-1$
