Question

tính C=a⁵-3a³

Với a=\(\sqrt{3+2\sqrt{2}+\sqrt{3-2\sqrt{2}}}\)

Answer 1

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

\(a^2=2+3\sqrt{2}\)

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

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

lẻ quá