Đáp án:
$P=2028.$
Giải thích các bước giải:
$x=\sqrt[3]{5-2\sqrt{6}}+\sqrt[3]{5+2\sqrt{6}}\\ x^3=\left(\sqrt[3]{5-2\sqrt{6}}+\sqrt[3]{5+2\sqrt{6}}\right)^3\\ =5-2\sqrt{6}+5+2\sqrt{6}+3\sqrt[3]{5-2\sqrt{6}}^2\sqrt[3]{5+2\sqrt{6}}+3\sqrt[3]{5-2\sqrt{6}}\sqrt[3]{5+2\sqrt{6}}^2\\ =10+3\sqrt[3]{5-2\sqrt{6}}\sqrt[3]{5+2\sqrt{6}}\left(\sqrt[3]{5-2\sqrt{6}}+\sqrt[3]{5+2\sqrt{6}}\right)\\ =10+3\sqrt[3]{(5-2\sqrt{6})(5+2\sqrt{6})}x\\ =10+3\sqrt[3]{25-24}x\\ =10+3x\\ \Leftrightarrow x^3=10+3x\\ \Leftrightarrow x^3-3x=10\\ P= x^3-3x+2018=10+2018=2028.$
