off to infinity

8 posts in this topic

Posted · Report post

Evaluate the following expression

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

0

Share on other sites

Posted · Report post

2?

0

Share on other sites

Posted · Report post

2?

correct. Care to explain your solution?

0

Share on other sites

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.

0

Share on other sites

Posted · Report post

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

then

...

0

Share on other sites

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!

0

Share on other sites

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

0

Share on other sites

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))

0

Create an account

Register a new account