Question

√√3+√19-8√3 demonstrati ca valoarea expresiei este un numar natural va roog

Answer 1

[tex]\it a = \sqrt{\sqrt3+\sqrt{19-8\sqrt3}} \ \ \ \ \ (1) \\\;\\ \\\;\\ \sqrt{19-8\sqrt3} = \sqrt{16-8\sqrt3+3} = \sqrt{(4-\sqrt3)^2} =4-\sqrt3 \ \ \ \ (2) \\\;\\ \\\;\\ (1), (2) \Rightarrow a = \sqrt{\sqrt3+4-\sqrt3} = \sqrt4 = 2 \in \mathbb{N}[/tex]