+2653 Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.
+129881 a^3 + 3ab^2 = 679 (1)
3a^3 - ab^2 = 615 → 9a^3 - 3ab^2 = 1845 (2)
Add (1) , (2) and we have
10a^3 = 2524
a^3 = 2524 / 10
a = (252.4)^(1/3)
Sub this into (1)
(2524/10) + 3 (252.4)^(1/3) b^2 = 679 solving this for b produces
b = -4.74353 or b = 4.74353
a - b = ( 252.4)^(1/3) + 4.74353 ≈ 11.06
a - b = (252.4)^(1/3) - 4.74353 ≈ 1.576
