calculating the value of golden ratio given by the nested radical equation

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Fermat · Answer 1 · 2015-11-10T06:47:37+0000

Φ = sqrt(1+sqrt(1+sqrt(1+sqrt(1+…

Φ^2 = 1+sqrt(1+sqrt(1+sqrt(1+…

Φ^2 - 1 = sqrt(1+sqrt(1+sqrt(1+…

And using the very first line,

Φ^2 - 1 = Φ

Φ^2 - Φ - 1 = 0

Using the quadratic formula,

Φ = (1 +/- sqrt(1^2 - 4(1)(-1)))/(2)

Φ = (1 +/- sqrt(1+ 4))/(2)

Φ = (1 +/- sqrt(5))/(2)

calculating the value of golden ratio given by the nested radical equation

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