Math challenge #2 - Find the value of these recurring square roots
Question
(Difficulty: 4/10)
Find the value of 
Who can get it right first? Provide your answer with steps in the comments below! :)
Solution
(Difficulty: 4/10)
Find the value of
Who can get it right first? Provide your answer with steps in the comments below! :)
Thanks for your participation guys! Seems that all of you are able to figure out the answer. Please see my solution in the main post :)
The series of square roots includes itself, i.e.:
sqrt(3+x) = x
3 + x = x^2
x^2 - x - 3 = 0
x = 1/2 + sqrt(13)/2 ≈ 2.30277563773
x = 1/2 - sqrt(13)/2 ≈ -1.30277563773
One thing to add,
The answer is 2.30277563773 instead of -1.30277563773
because the original expression is a square root, which is always >0 (i guess)
Oh you spotted the same thing nearly at the same time as me haha
I agree with the positive answer:
You are on the right track! But at the end you arrived at 2 values, then which one is the correct one? :)
A square root has always two answers, one positive and one negative. For example, sqrt(9) can be either 3 or -3; both are correct. However, for this series to be convergent, we must always choose either positive or negative roots. In the former case, we get the first result, and in the latter case, the second result.
from what ive learned,
if the question says x^2 =9, then x can be either 3,-3 of coz
but if the question says x = sqrt(9), then x is unique and should be 3 but not -3
I think sqrt(9) only equal to 3?
x^2 = 9 => x = +- sqrt(3)
sqrt(3) is always sqrt(3), which is a positive number
Let the required expression be x, then we have a quadratic equation. Solving, we have x=(1+sqrt(13))/2
(The other root is rejected because it's negative)