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 = ?


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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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