Q. 7
The product of three numbers in G.P. is 216. If 2, 8, 6 be added to them, the results are in A.P. Find the numbers.
Answer :
Let the three numbers be 
.
∴ According to the question
⇒ 
…(1)
⇒ a3 = 216
⇒ a = 6
2,8,6 is added to them
∴ 
The above sequence is in AP.
We know in AP.
2b = a + c
⇒ 
Substituting a = 6 in above equation we get,
⇒ 
⇒ 
⇒ 28r = 6 + 6r2 + 8r
⇒ 6r2 – 20r + 6 = 0
⇒ 6r2 – 18r – 2r – 6 = 0
⇒ 6r(r – 3) – 2(r – 3) = 0
⇒ (6r – 2) (r – 3) = 0
⇒ r = 3 or r = 1/3 .
∴ Now the equation will be
⇒ 
⇒ 2,6,18 or 18,6,2
∴ The three numbers are 2,6,18.
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