If a + b = 7 and a^3 + b^3 = 45, what is the value of the sum 1/a + 1/b? Express your answer as a common fraction.
+128408 a + b = 7
Square both sides
a^2 + 2ab + b^2 = 49
a^2 + b^2 = 49 - 2ab
a^3 + b^3 = (a + b) (a^2 - ab + b^2) = 45
(a + b) ( a^2 + b^2 - ab) = 45
(7) ( 49 - 2ab - ab) = 45
49 - 3ab = 45/7
49 - 45/7 = 3ab
298/7 = 3ab
298 / 21 = ab
And
1/a + 1/b = (a + b) / ab = 7 / (298/21) = 147 / 298
