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Match the set of values of x in List-II which satisfy the equations in List-I.
List- I
List- II
(P) $x^{4} - x^{2} - 2 x - 1 = 0$ (1)
$2 \cos 36^{\circ}$
(Q) $x^{4} + x^{3} - 2 x^{2} - x + 1 = 0$ (2)
$2 \sin 18^{\circ}$
(R) $x^{4} - 5 x^{2} + 5 = 0$ (3)
$2 \sin 36^{\circ}$
(S) $x^{3} - x^{2} - 3 x + 2 = 0$ (4)
$2 \cos 18^{\circ}$

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P-4, Q-2, R-4, S-2

P-1, Q-2, R-3, S-2

P-1, Q-2, R-4, S-1

P-2, Q-2, R-4, S-2

answer is A.

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Detailed Solution

P) Put $\frac{x^{2}}{x + 1} = t ∴ x = \frac{1 \pm \sqrt{5}}{2}$
Q) Put $x^{2} + x = t ∴ x = \frac{- 1 \pm \sqrt{5}}{2}$
R) $x^{2} = \frac{5 \pm \sqrt{5}}{2}$
S) $x = \frac{- 1 \pm \sqrt{5}}{2}$

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