If y = sqrt(5+sqrt(5-y)), find the value of y. Hint: The value is irrational

Question

Answer 1

square it and take 5 on another side and again square it.

Answer 2

square it and take 5 on another side and again square it.

Answer 3

y^4 - 10y^2 + y + 20 = 0
letting y^2=k
k^2 - 10k + sqrt(k) + 20 = 0
Don't know how to proceed ahead

Answer 4

y^4 - 10y^2 + y + 20 = 0
letting y^2=k
k^2 - 10k + sqrt(k) + 20 = 0
Don't know how to proceed ahead

Answer 5

What is the answer?

Answer 6

What is the answer?