CBSE Class 12-science Answered
Find 3 numbers in GP whose product is 729 and sum of their products in pairs is 819.
Asked by coolameet08 | 14 Feb, 2010, 12:39: PM
Expert Answer
Let the three numbers be a, ar, ar2.
a3r3 = 729
ar = 9
a(ar)+ar(ar2)+a(ar2) = 819
a2r + a2r3 + a2r2 = 819
81/r + 81r + 81 = 819
1/r + r + 1 = 91/9
1/r + r = 82/9
r2 - 82r/9 + 1 = 0
9r2 - 82r + 9 = 0
r = {82±
(6724 - 324)}/18
= 9 and 1/9
Hence the three numbers are, 1, 9, 81.
Regards,
Team,
TopperLearning.
Answered by | 14 Feb, 2010, 02:03: PM
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