Correct Answer: (1) -3/4 या -4/3
Note: माना, गुणोत्तर श्रेणी में तीन संख्याएँ = a/r, a, ar
प्रश्नानुसार,
a/r + a + ar = 13/12 .....(i)
एवं, a/r × a × ar = -1
= a^3 = -1
= a = -1
समीकरण (i) से,
-1/r + (-1) - r = 13/12
= -1/r - 1 - r = 13/12
= (-1 - r - r^2)/r = 13/12
= -12 - 12r - 12r^2 = 13r
= -12 - 25r - 12r^2 = 0
= 12r^2 + 25r + 12 = 0
∴ r = -25 ± √[(25)^2 - 4 × 12 × 12] / [2 × 12]
= -25 ± √(625 - 576) / 24
= -25 ± √49 / 24
= -25 ± 7 / 24
∴ r = (-25 + 7) / 24 = -18 / 24 = -3 / 4
या, r = (-25 - 7) / 24 = -32 / 24 = -4 / 3