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Question

Find three numbers in G.P. whose product is 729 and the sum of their products in pairs is 819.


Solution

Let three numbers in G.P. are ar,a,ar

Here,

ar×a×ar=729

a3=729

a=9

And (ar×a)+(a×ar)+(ar×ar)=819

81r+81r+81=819

9r+9r+9=91

9+9r2+9=91

9r282r+9=0

9r281rr+9=0

9r(r9)1(r9)=0

r=9,19

Hence, putting the value of a and r, we get the number to be 81, 9 and 1 or 1, 9 and 81.

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