Let and be the roots of x2 + 3x - 16 = 0, and and be the roots of x2 + 3x - 1 = 0. If Pn = n + n and Qn = n + n, then P25 + 3P242P23 + Q25 - Q23Q24 is equal to
(3) 5
∵ 2 + 3 - 16 = 0 ⇒ 25 + 3 24 = 16 23 (similarly for )
⇒ P25 + 3P24 = 16P23
∵ 2 + 3 - 1 = 0 ⇒ 25 - 23 = -3 24 (similarly for )
⇒ Q25 - Q23 = -3Q24
∴ Required value = 16P232P23 + -3Q24Q24 = 8 - 3 = 5
Answer: (3)
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