Question

Exercițiul 3 va rog frumos
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Answer 1

Răspuns:

1

Explicație pas cu pas:

$a=(5-2\sqrt{6})^{1009}*(\sqrt{2}+\sqrt{3})^{2018}*(7-4\sqrt{3})^{100}*(\sqrt{3}+2)^{200}\\a=(5-2\sqrt{6})^{1009}*[(\sqrt{2}+\sqrt{3})^2]^{1009}*(7-4\sqrt{3})^{100}*[(\sqrt{3}+2)^2]^{100}\\a=(5-2\sqrt{6})^{1009}*(2+2\sqrt{6}+3)^{1009}*(7-4\sqrt{3})^{100}*(3+4\sqrt{3}+4)^{100}\\a=(5-2\sqrt{6})^{1009}*(5+2\sqrt{6})^{1009}*(7-4\sqrt{3})^{100}*(7+4\sqrt{3})^{100}\\a=[(5-2\sqrt{6})*(5+2\sqrt{6})]^{1009}*[(7-4\sqrt{3})*(7+4\sqrt{3})]^{100}\\a=(25-24)^{1009}*(49-48)^{100}\\a=1^{1009}*1^{100}\\a=1$