Question

The product of three numbers in G.P. is 216 and sum of their squares is 651. Find the numbers​

Answer 1

Answer:

Let the numbers in G.P are,

r

a

,a,ar

⇒a=5

Also, a

2

(

r

1

.1+1.r+r.

r

1

)=

2

175

or

25(r

2

+r+1)=

2

175

r

or 2(r

2

+r+1)=7r

or 2r

2

−5r+2=0

or (r−2)(2r−1)=0

∴r=2,

2

1

Hence the numbers are 10,5,5/2 or 5/2,5,10

Answer 2

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.

Step-by-step explanation: