Question

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

Answer 1

Let the three terms of G.P be

r

a

,a,ar

Common ratio =r

Given :

r

a

×a×ar=216

⇒a

3

=216=6

3

∴a=6

Now,

r

a

×a+a×ar+ar×

r

a

=156 .... [Given]

⇒a

2

(r+1+

r

1

)=156

⇒36(r+1+

r

1

)=156

3r

2

+3r+3=13r

3r

2

−10r+3=0

⇒r=3,

3

1

Let us take r=3

The, the numbers are

3

6

,6,6.3 i.e. 2,6,18.

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