+766 Find all real numbers a and b such that
a + b = 14
a^3 + b^3 = 812 + a^2 + b^2
+6 Couldn't you just substitute a=-14-b into the second equation and then factor/solve the cubic?
+130458 a + b = 14
b = 14 - a
a^3 + (14 -a)^3 = 812 + a^2 + (14 -a)^2
a^3 - a^3 + 42a^2 -588a + 2744 = 812 + a^2 + a^2 - 28a + 196
40a^2 - 560a + 1736 = 0
5a^2 - 70a + 217 = 0
a = [ 70 + sqrt [ 70^2 - 20*217] ] / 10 = [ 70 + sqrt [ 15260] ] / 10 = [ 70 + 2sqrt 35 ] / 10 =
7 + sqrt (35) / 5
And b = 7 - sqrt(35) / 5
Also a = 7 - sqrt (35) / 5 and b = 7 + sqrt (35) / 5
