Trigonometric Functions · Question 22

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The number of solutions of the equation 2 2 + 5 2 = 2 3 5 2 in [- 2, 2 ] is :

Answer

(2) 7

Using 4 3 A = 3A + 3 A with A = 5 2:

2 3 5 2 = 12 ( 15 2 + 3 5 2 )

2 2 2 + 2 5 2 = 15 2 + 3 5 2

2 2 2 = 15 2 + 5 2

2 2 2 = 5 2 + 3 2

3 2 = 15 2

15 2 = 2n 3 2, n Z

6 = 2n or 9 = 2n

= n 3 or = 2n 9

In [- 2, 2 ]:

= n 3: 0, 3

= 2n 9: 0, 2 9, 4 9

Distinct solutions: 0, 3, 2 9, 4 9 7 solutions

Answer: (2)

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