Find 3 numbers in GP whose product is 729 and sum of their products in pairs is 819.

Asked by coolameet08 | 14th 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.

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Answered by  | 14th Feb, 2010, 02:03: PM

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