Question

Cum pot rezolva acest exercitiu cu ajutorul formulelor de calcul prescurtat?
(√3+√2+√5 -1)(√3+√2+√5+1)

Answer 1

$( \sqrt{3} + \sqrt{2} + \sqrt{5} - 1)( \sqrt{3} + \sqrt{2} + \sqrt{5} + 1) = \\ \\ \sqrt{3}( \sqrt{3} + \sqrt{2} + \sqrt{5} - 1) + \sqrt{2}( \sqrt{3} + \sqrt{2} + \sqrt{5} + 1) + \sqrt{5}( \sqrt{3} + \sqrt{2} + \sqrt{5} + 1) - \sqrt{3} - \sqrt{2} - \sqrt{5} - 1 = \\ \\ 3 + \sqrt{6} + \sqrt{15} + \sqrt{3} + \sqrt{6} + 2 + \sqrt{10} + \sqrt{2} + \sqrt{15} + \sqrt{10} + 5 + \sqrt{5} - \sqrt{3} - \sqrt{2} - \sqrt{5} - 1 = \\ \\ (3 + 2 + 5 - 1) + ( \sqrt{6} + \sqrt{6}) + ( \sqrt{15} + \sqrt{15}) + ( \sqrt{3} - \sqrt{3}) + ( \sqrt{10} + \sqrt{10}) + ( \sqrt{2} - \sqrt{2}) + ( \sqrt{5} - \sqrt{5}) = \\ \\ 9 + 2 \sqrt{6} + 2 \sqrt{15} + 2 \sqrt{10}$