Răspuns:
1
Explicație pas cu pas:
[tex]a=(5-2\sqrt{6})^{1009}*(\sqrt{2}+\sqrt{3})^{2018}*(7-4\sqrt{3})^{100}*(\sqrt{3}+2)^{200}\\a=(5-2\sqrt{6})^{1009}*[(\sqrt{2}+\sqrt{3})^2]^{1009}*(7-4\sqrt{3})^{100}*[(\sqrt{3}+2)^2]^{100}\\a=(5-2\sqrt{6})^{1009}*(2+2\sqrt{6}+3)^{1009}*(7-4\sqrt{3})^{100}*(3+4\sqrt{3}+4)^{100}\\a=(5-2\sqrt{6})^{1009}*(5+2\sqrt{6})^{1009}*(7-4\sqrt{3})^{100}*(7+4\sqrt{3})^{100}\\a=[(5-2\sqrt{6})*(5+2\sqrt{6})]^{1009}*[(7-4\sqrt{3})*(7+4\sqrt{3})]^{100}\\a=(25-24)^{1009}*(49-48)^{100}\\a=1^{1009}*1^{100}\\a=1[/tex]
