Question

HELP ME OR DIE

Answer 1

1.

\(A=\sqrt[3]{6\sqrt{3}+10}-\sqrt[3]{6\sqrt{3}-10}\)

\(=\sqrt[3]{\left(\sqrt{3}+1\right)^3}-\sqrt[3]{\left(\sqrt{3}-1\right)^3}\)

\(=\sqrt{3}+1-\sqrt{3}+1=2\)

Answer 2

2.

\(B=\sqrt{3+\sqrt{3}+\sqrt[3]{6\sqrt{3}+10}}\)

\(=\sqrt{3+\sqrt{3}+\sqrt[3]{\left(\sqrt{3}+1\right)^3}}\)

\(=\sqrt{3+\sqrt{3}+\sqrt{3}+1}\)

\(=\sqrt{4+2\sqrt{3}}\)

\(=\sqrt{\left(\sqrt{3}+1\right)^2}=\sqrt{3}+1\)

Answer 3

3.

\(C=\dfrac{2}{\sqrt[3]{3}-1}-\dfrac{4}{\sqrt[3]{9}-\sqrt[3]{3}+1}\)

\(=\dfrac{2\left(\sqrt[3]{9}-\sqrt[3]{3}+1\right)-4\left(\sqrt[3]{3}-1\right)}{\left(\sqrt[3]{3}-1\right)\left(\sqrt[3]{9}-\sqrt[3]{3}+1\right)}\)

\(=\dfrac{2\sqrt[3]{9}-2\sqrt[3]{3}+2-4\sqrt[3]{3}+4}{3-1}\)

\(=\sqrt[3]{9}-3\sqrt[3]{3}+3\)