In a G.P the product of three consecutive terms is 27 and the sum of the product of two terms taken at a time is 572.Find the three terms.
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Answer:
The three terms are either 2, 3, 9/2 or 9/2, 3, 2.
Step-by-step explanation:
Let three consecutive terms of a GP are a/r, a, ar.
Product of three consecutive terms is 27.
a/r ×r×ar = 27
a^3 = 27
a = 3
The sum of the product of two terms taken at a time is 57/2.
a/r*a+a*ar+a/r*ar = 57/2
a^2/r + a^2r + a^2 = 57/2
Substitute a = 3
3^2/r + 3^2r + 3^2 = 57/2
9/r + 9r + 9 = 57/2
9 + 9r^2 / r= 57/2 - 9
9 + 9r^2 / r = 39/2
18 + 18r^2 = 39r
18r^2 - 39r + 18 = 0
(2r-3) (9r-6) = 0
r = 3/2, 2/3
For a = 3 and r = 3/2 and three terms are 2, 3, 9/2....
For a = 3 and r = 2/3 and three terms are 2, 3, 9/2....
Therefore, the three terms are either 2, 3, 9/2 or 9/2, 3, 2.
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