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Let a and b be real numbers such that a + b = 4 and a^4 + b^4 = 16.

(a) Find all possible values of ab
(b) Find all possible values of a + b
(c) Find all possible values of a and b

1 answer

(a) All possible values of ab are 0.

(b) All possible values of a + b are 4.

(c) All possible values of a and b are a = 2 and b = 2, or a = -2 and b = 6.