Find all solutions to the system
a + b = 14,
a3 + b3 = 812.
a + b = 14 ---> a = 14 - b
a3 + b3 = 812 ---> (14 - b)3 + b3 = 812 (substitution)
[ 2744 - 3(142)b + 3(14)b2 - b3 ] + b3 = 812 (cubic expansion)
2744 - 588b + 42b2 = 812
42b2 - 588b + 1932 = 0
21b2 - 294b + 966 = 0
Now use the quadratic formula ...