perplexus.info :: Just Math : Root switching sides

Root switching sides (Posted on 2019-07-10)

Solve the equation

√(x+√(4x+√(16x+√(...+√(4²⁰¹⁹x+3)...))))-√x = 1

No Solution Yet Submitted by Danish Ahmed Khan

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By observation

| Comment 1 of 2

√(x+√(4x+3))-√x = 1: x=1/4

√(x+√(4x+√(16x+3)))-√x = 1 : x=1/16

√(x+√(4x+√(16x+√(64x+3))))-√x = 1: x=1/64

so for the given equation, x=1/4²⁰¹⁹(whatever that is).

Edited on July 10, 2019, 9:31 am

Posted by broll on 2019-07-10 09:30:04

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