+128474 a + b = 7
a^2 + 2ab + b^2 = 49
a^2 + b^2 = 49 - 2ab (1)
a^3 + b^3 = 42
(a + b)(a^2 - ab + b^2) = 42
(7) (a^2 - ab + b^2) = 42
a^2 - ab + b^2 = 6
a^2 + b^2 - ab = 6 (2)
Sub (1) into (2) and we have that
49 - 2ab - ab = 6
43 = 3ab
43/3 = ab
So
1/a + 1/b =
(a + b)
______ =
ab
7
______ =
(43/3)
21
__
43
