a-b-c-d-2-a-2-b-2-c-2-d-2-6-a-3-b-3-c-3-d-3-20-a-4-b-4-c-4-d-4-66-a-b-c-d-

Question Number 82030 by naka3546 last updated on 17/Feb/20

a - b + c - d = 2

a^{2} - b^{2} + c^{2} - d^{2} = 6

a^{3} - b^{3} + c^{3} - d^{3} = 20

a^{4} - b^{4} + c^{4} - d^{4} = 66

a + b + c + d = ?

Answered by MJS last updated on 17/Feb/20

let

a = α - \sqrt{β} \land c = α + \sqrt{β} \land b = γ - \sqrt{δ} \land d = γ + \sqrt{δ}

\Rightarrow we can easily solve the equations and find

{there}^{'} s only one solution

a = 1 \land b = 0 \land c = 3 \land d = 2

\Rightarrow a + b + c + d = 6

Commented by mr W last updated on 17/Feb/20

p e r f e c t s o l u t i o n s i r!

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