Question
A sequence is provided below.
Carefully analyze the given details and respond to the related query. Sequence: 134, 70, 38, 22, 2(r + y), (x + y), (y + 3) Equation I: p2 - 2xp + 8r = 0 Equation II: q2- 3(2x - y)q + 2(4r - 1) = 0 Determine the difference between the greatest root of Equation I and the smallest root of Equation II?Solution
ATQ, 134 - 26 = 70 70 - 25 = 38 38 - 24 = 22 22 - 23 = 14 = 2(r + y) 14 - 22 = 10 = (x + y) 10 - 21 = 8 = (y + 3) y = 8 - 3 = 5 x = 10 - 5 = 5 r = 14/2 - 5 = 7 - 5 = 2 Equation I, p2- 2xp + 8r = 0 p2 - 2 × 5p + 8 × 2 = 0 p2 - 10p + 16 = 0 (p - 2)(p - 8) = 0 p = 2, 8 Equation II, q2 - 3(2x - y)q + 2(4r - 1) = 0 q2 - 3(2 × 5 - 5)q + 2(4 × 2 - 1) = 0 q2 - 15q + 14 = 0 (q - 1)(q - 14) = 0 q = 1, 14 Difference = Larger root of equation I - Smaller root of equation II = 8 - 1 = 7
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