c, \(x=\sqrt[3]{22\sqrt{2}+25}-\sqrt[3]{22\sqrt{2}-25}\)
\(=\sqrt[3]{\left(2\sqrt{2}+1\right)^3}-\sqrt[3]{\left(2\sqrt{2}-1\right)^3}\)
\(=2\sqrt{2}+1-2\sqrt{2}+1=2\)
d, \(x=\dfrac{\sqrt[3]{8-3\sqrt{5}}+\sqrt[3]{64-12\sqrt{20}}}{\sqrt[3]{57}}.\sqrt[3]{8+3\sqrt{5}}\)
\(=\dfrac{\sqrt[3]{8-3\sqrt{5}}+\sqrt[3]{8\left(8-3\sqrt{5}\right)}}{\sqrt[3]{57}}.\sqrt[3]{8+3\sqrt{5}}\)
\(=\dfrac{\sqrt[3]{64-45}+2\sqrt[3]{64-45}}{\sqrt[3]{57}}\)
\(=\dfrac{3\sqrt[3]{19}}{\sqrt[3]{19}.\sqrt[3]{3}}=\sqrt[3]{9}\)
e, \(P=x^3+3x^2+3x+10\)
\(=\left(x+1\right)^3+9\)
\(=\left(\sqrt[3]{2}-1+1\right)^3+9=11\)
