Trigonometric Functions · Question 25

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The number of solutions of the equation (4 - 3) x - 2 3 2 x = - 41 + 3, x [-2 , 5 2 ] is

Answer

(4) 5

41 + 3 = 4( 3 - 1)2 = 2 3 - 2

Put 2 x = 1 - 2 x:

(4 - 3) x - 2 3 + 2 3 2 x = -2 3 + 2

⇒ 2 3 2 x + (4 - 3) x - 2 = 0

Discriminant = (4 - 3)2 + 16 3 = 19 + 8 3 = (4 + 3)2

⇒ x = -(4 - 3) (4 + 3)4 3

⇒ x = 12 or x = - 2 3 (rejected, since 2 3 > 1)

x = 12 in [-2 , 5 2 ]:

x = - 11 6, - 7 6, 6, 5 6, 13 6

( 17 6 > 5 2 is outside the interval)

∴ Number of solutions = 5

Answer: (4)

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