+12 Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.
+129933 a^3 + 3ab^2 = 675
(675 - a^3) / 3 = ab^2
Subbing this into the second equation we have
3a^3 - (675 - a^3)/3 = 615 multiply through by 3
9a^3 -675 -+ a^3 = 1845
10a^3 = 2520
a^3 = 2520/10
a = (252)^(1/3) ≈ 6.316
Using the first equation
252 + 3(6.316)*b^2 = 675
18.948b^2 = 423
b = sqrt [ 423 / 18.948 ] ≈ 4.725 or -4.725
a - b = 6.316 - 4.725 ≈ 1.591
or
a - b = 6.316 - (-4.725) ≈ 11.041
