+28 If a + b = 1 and a^2 + b^2 = 2, what is the value of a^3 + b^3? Express your answer as a common fraction.
+129839 f a + b = 1 and a^2 + b^2 = 2, what is the value of a^3 + b^3? Express your answer as a common fraction.
If a + b = 1....square both sides
a^2 + 2ab + b^2 = 1
(a^2 + b^2) + 2ab = 1
2 + 2ab = 1
2ab = 1- 2
2ab = -1
ab = -1/2 → -ab = 1/2
So
a^3 + b^3 =
(a + b) (a^2 - ab + b^2) =
(a + b) ( [a^2 + b^2] - ab) =
(1) ( 2 + 1/2) =
(1)( 5/2) =
5 / 2
