An algebra problem [Romania 1974]

Algebra Level 2

\[\large \sqrt{a+bx} + \sqrt{b+cx} + \sqrt{c+ax} = \sqrt{b-ax} + \sqrt{c-bx} +\sqrt{a-cx} \]

Let \(a,b\) and \(c\) be real and positive parameters. Solve the equation above. What is the value of \(x\)?

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