The product of three numbers in G.P. is 216 and sum of their squares is 651. Find the numbers
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Answer:
Let the required numbers be
a
r
, a and ar. Then,
a
r
×
a
×
a
r
=
216
⇒
a
3
=
216
=
6
3
⇒
a
=
6
And,
a
r
×
a
+
a
×
a
r
+
a
r
×
a
r
=
156
⇒
a
2
(
1
r
+
r
+
1
)
=
156
⇒
(
6
2
)
(
1
+
r
+
r
2
)
=
156
r
[
∵
a
=
6
]
⇒
36
(
r
2
+
r
+
1
)
=
156
r
⇒
3
(
r
2
+
r
+
1
)
=
13
r
⇒
3
r
2
−
10
r
+
3
=
0
⇒
(
3
r
−
1
)
(
r
−
3
)
=
0
⇒
r
=
1
3
or
r
=
3
So, the required numbers are 18, 6, 2 or 2, 6, 18.
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