By putting "solve(a + b = 14, a^3 + b^3 = 812 + a^2 + b^2)" into the calculator, I got (a = - (2 x squareroot(35) - 35) / 5), (a = + (2 x squareroot(35) + 35) / 5), (b = - (2 x squareroot(35) - 35) / 5), (b = + (2 x squareroot(35) + 35) / 5). I hope this awnsers your question.
