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Question

Question: \(\sqrt{- 1 - \sqrt{- 1 - \sqrt{- 1 - ...to\infty}}}\) =...

−1−−1−−1−...to∞\sqrt{- 1 - \sqrt{- 1 - \sqrt{- 1 - ...to\infty}}} =

A

1

B

–1

C

–w

D

w2

Answer

w2

Explanation

Solution

Sol. Let x = −1−−1−−1−.......∞\sqrt{- 1 - \sqrt{- 1 - \sqrt{- 1 - .......\infty}}}

Then x = −1−x\sqrt{- 1 - x}; or x2 = – 1 – x ; x2 + x + 1 = 0

x =−1±−32\frac{- 1 \pm \sqrt{- 3}}{2}= w or w2