Square root question, please help! Thank you!
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Square root question, please help! Thank you!

[From: ] [author: ] [Date: 11-09-20] [Hit: ]
.,x = sqrt(2 + (√2+√2+√2+√2...x = 2,......
Find value of √2+√2+√2+√2...
sorry, I have hard time to type the question. √2+ is inside square root another √2+, not answer 4√2.Hope you understand my question.

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Let x = √2+√2+√2+√2..., then

x = sqrt(2 + (√2+√2+√2+√2...) )
= sqrt(2 + x)

x^2 - x - 2 = 0

(x-2)(x+1) = 0

x = 2, or -1. Since x must be > sqrt(2) > 0, the root -1 is dropped.

The answer is x = 2.
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