find three numbers in G.P such that their product is 512 and the sum of first and third number is 34
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Let the three numbers in G.P. be a,ar,ar
2
.
Then,
a×ar×ar
2
=512
(ar)
3
=512
ar=8
Now,
2
(a+4)+ar
2
=ar+4
a+ar
2
+4=2ar+8
Putting r=
a
8
, we get,
a+
a
64
=20
a
2
−20a+64=0
a
2
−16a−4a+64=0
a(a−16)−4(a−16)=0
(a−16)(a−4)=0
a=16,4
Therefore, numbers are 4,8,16 or 16,8,4.
Sum of numbers = 4+8+16=28.
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