If a + b = 7 and a^3 + b^3 = 42 + ab, what is the value of the sum 1/a + 1/b? Express you answer as a common fraction.
1/a + 1/b = 4/17.
(a + b) = 7 cube both sides
a^3 + 3a^2b + 3ab^2 + b^3 = 343
a^3 + b^3 + 3ab ( a + b) = 343
42 + ab + 3ab ( 7) = 343
42 + 22ab = 343
22ab = 301
ab = 301 / 22
And
1/a + 1/b = [ a + b ] / ab = 7 / ( 301/22) = 22 * 7 / 301 = 154 / 301 = 22 / 43
