SOLUTION: x2 - x - 1 = 0 Let x = j j2 - j - 1= 0 Isolate j2 j2 = 1 + j Take the square root of both sides j= √1 + j Now we know that the value of j is 1 + j j= √1 +

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Question 1161304: x2 - x - 1 = 0 Let x = j
j2 - j - 1= 0 Isolate j2
j2 = 1 + j Take the square root of both sides
j= √1 + j Now we know that the value of j is 1 + j
j= √1 + √1+⋯
Iteration #1: j= √1 + √1
Iteration #2: j= √1 + √1+√1
Show how we can use iterations of this nested radical to find the value of j. How many iterations do we need to do to get close to the value we calculated in 1)?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


No. Your entire premise is faulty.



Let

Ok, but the substitution has no value that I can see.



Isolate

That's ok

Take the square root of both sides

Here is where you go high and right:





The idea that is ludicrous. If that were true, you could subtract j from both sides and get 0 = 1.

The rest of your post is nonsense.

I think what you were trying to get to was:



In which case you need at least 10 iterations to be correct to the 4th decimal place. This method converges very slowly.

The 19th Fibonacci number divided by the 18th Fibonacci number gets you 5 decimal place accuracy with a crapload less arithmetic.


John

My calculator said it, I believe it, that settles it