What is n?

Algebra Level 5

x+2x+2x++2x+23x n radical signs =x\underbrace{ \sqrt{ x+2\sqrt{x+2\sqrt{x+\ldots +2\sqrt{x+2\sqrt{3x}}}}}}_{\large \text{ n radical signs }}=x

Find the average of all the real roots of the equation above for a natural number n>1n>1.

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