Let a and b be real numbers such that a^3 + 3ab^2 = 679 and a^3 - 3ab^2 = 673. Find a - b.
+1632 These are a system of equations. Add the first two equations, and you get 2a^3 (the 3ab^2 cancel each other out) = 1352. a^3 = 676.
a = cube root of 676.
Plugging back in, we have 676 + 3cbrt(676)b^2 = 679
cbrt(676)b^2 = 1
1/cbrt(676)
b = sqrt(cbrt(676^2)/676) = cbrt(676)/26
a - b = cbrt(676) - cbrt(676) = 25cbrt(676)/26
