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α = sin 36 ° is a root of which of the following equation

Options

  1. A16 x 4 - 20 x 2 + 5 = 0
  2. B16 x 4 + 20 x 2 + 5 = 0
  3. C10 x 4 - 10 x 2 - 5 = 0
  4. D16 x 4 - 10 x 2 + 5 = 0

Correct answer

A. 16 x 4 - 20 x 2 + 5 = 0

Step-by-step solution

We know sin 36 ° = 10 - 2 5 4 Let x = 10 - 2 5 4 On squaring both sides, we get 4 x 2 = 10 - 2 5 ⇒ 16 x 2 = 10 - 2 5   Again squaring, we get 5 2 = 5 - 8 x 2 2 ⇒ 5 = 25 + 64 x 4 - 80 x 2 ⇒ 16 x 4 - 20 x 2 + 5 = 0

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