JEE Main | 2014Binomial TheoremMedium
Question
Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is
Options
A.2 - √3
B.2 + √3
C.√2 + √3
D.3 + √2
Solution
a, ar, ar2 → G.P.
a, 2ar, ar2 → A.P.
2 × 2ar = a + ar2
4r = 1 + r2
⇒ r2 - 4r + 1 = 0
r =
= 2 ± √ 3
r = 2 - √3 is rejected
∵ (r > 1)
G.P. is increasing.
a, 2ar, ar2 → A.P.
2 × 2ar = a + ar2
4r = 1 + r2
⇒ r2 - 4r + 1 = 0
r =
= 2 ± √ 3r = 2 - √3 is rejected
∵ (r > 1)
G.P. is increasing.
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