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off to infinity

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Evaluate the following expression

sqrt(2+sqrt(2+sqrt(2+sqrt(2+... repeating forever.

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Posted · Report post

2?

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2?

correct. Care to explain your solution?

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Posted · Report post

2?

correct. Care to explain your solution?

Calculator.

Every +sqrt(2) I pasted into the equation returned an answer that edged closer and closer to 2. It was more of a guess than an answer.

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Posted · Report post

let x = sqrt(2+sqrt(2+sqrt(2+sqrt(2+...

then

...

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Posted · Report post

let x = sqrt(2+sqrt(2+sqrt(2+sqrt(2+...

then

...

I hope you're not intimating that -1 is also a solution!

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Posted (edited) · Report post

let x = sqrt(2+sqrt(2+sqrt(2+sqrt(2+...

then

...

I hope you're not intimating that -1 is also a solution!

nice work, but clearly -1 is a false solution and should be disregarded as such leaving only 2

Edited by BMAD
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Posted · Report post

to expand on superprismatic

let x = sqrt(2+sqrt(2+sqrt(2+sqrt(2+...

so

x = sqrt(2 + x)

x^2 = 2 + x

x^2 - x - 2 = 0

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

x =2, x =-1

x=-1 is impossible as the sqrt cannot give a negative answer (i.e. -1 = sqrt(1))

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