Question

7-3√2   +  7+3√2  =
7+3√2     7-3√2

Answer 1

$frac{7-3 sqrt{2} }{7+3 sqrt{2} } + frac{7+3 sqrt{2} }{7-3 sqrt{2} } = (frac{(7-3 sqrt{2}) ^{2}+(7+3 sqrt{2}) ^{2} }{(7+3 sqrt{2})(7-3 sqrt{2}) }= frac{49-42 sqrt{2} +18+49 +42 sqrt{2} +18}{49-9cdot 2} = \ = frac{134}{31}=4 frac{10}{31}$