Question

Sa se arate ca √28+(1+√2)²-√8+(1-√7)² este numar natural prim. Intreaga rezolvare va rog.

Answer 1

$\sqrt{28} + {(1 + \sqrt{2}) }^{2} - \sqrt{8} + {(1 - \sqrt{7}) }^{2} = \\ \\ 2 \sqrt{7} + {(1 + \sqrt{2}) }^{2} - 2 \sqrt{2} + {(1 - \sqrt{7}) }^{2} = \\ \\ 2 \sqrt{7} + 1 + 2 \sqrt{2} + { \sqrt{2} }^{2} - 2 \sqrt{2} + 1 - 2 \sqrt{7} + { \sqrt{7} }^{2} = \\ \\ 2 \sqrt{7} + 1 + 2 \sqrt{2} + 2 - 2 \sqrt{2} + 1 - 2 \sqrt{7} + 7 = \\ \\ (2 \sqrt{7} - 2 \sqrt{7}) + (1 + 2 + 1 + 7) + (2 \sqrt{2} - 2 \sqrt{2}) = \\ \\ 11$