3a-b-c-d-2014-3b-a-c-d-2014-3c-a-b-d-2014-3d-a-b-c-2014-Find-all-the-solution-of-a-b-c-d-if-a-b-c-d-R-

Question Number 9523 by Joel575 last updated on 12/Dec/16

3 a = {(b + c + d)}^{2014}

3 b = {(a + c + d)}^{2014}

3 c = {(a + b + d)}^{2014}

3 d = {(a + b + c)}^{2014}

Find all the solution of (a, b, c, d) if a, b, c, d \in R

Answered by mrW last updated on 16/Dec/16

let u = a + b + c + d

\Rightarrow 3 a = {(u - a)}^{2014}

\Rightarrow 3 b = {(u - b)}^{2014}

\Rightarrow 3 c = {(u - c)}^{2014}

\Rightarrow 3 d = {(u - d)}^{2014}

\Rightarrow a = b = c = d = x

3 x = {(3 x)}^{2014}

\Rightarrow x = 0

\Rightarrow {(3 x)}^{2013} = 1

\Rightarrow 3 x =^{2013} \sqrt{1} = 1

\Rightarrow x = \frac{1}{3}

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