If a + b = 7 and a^3 + b^3 = 44, what is the value of the sum 1/a + 1/b? Express your answer as a common fraction.
+129850 a + b = 7 square both sides
a^2 + 2ab + b^2 = 49
a^2 + b^2 = 49 - 2ab
and
a^3 + b^3 = 44
(a + b) ( a^2 - ab + b^2) = 44
(7) ( a^2 + b^2 - ab) = 44
(7) (49 - 2ab - ab) = 44
49 - 3ab = 44/7
49 - 44/7 = 3ab
299 / 7 = 3ab divide both sides by 3
299 / 21 = ab
1/a + 1/b = (a + b) /ab = 7 / ( 299/21) = 147 / 299
