Răspuns:
Explicație pas cu pas:
[tex][(7-4\sqrt{3})^{2019}+\dfrac{1}{(7-4\sqrt{3})^{2019}}]*(2(7+4\sqrt{3}))^{2019} =\dfrac{(7-4\sqrt{3})^{2019}(7+4\sqrt{3})^{2019}+1}{(7+4\sqrt{3})^{2019}} *2^{2019}*(7+4\sqrt{3})^{2019}=\dfrac{[(7-4\sqrt{3})(7-4\sqrt{3})]^{2019}+1}{(7+4\sqrt{3})^{2019}}* 2^{2019}*(7+4\sqrt{3})^{2019}=\\=\dfrac{[7^{2}-(4\sqrt{3})^{2}]^{2019}+1 }{(7+4\sqrt{3})^{2019}}* 2^{2019}*(7+4\sqrt{3})^{2019}=\dfrac{1^{2019}+1 }{(7+4\sqrt{3})^{2019}}* 2^{2019}*(7+4\sqrt{3})^{2019}=2^{2020}=(2^{1010})^{2}[/tex]Deci este p.p.
