Q. 2
Find three number in G.P. whose sum is 38 and their product is 1728.
Answer :
Let the three numbers be 
.
∴ According to the question
⇒ 
…(1)
⇒ 
…(2)
From 2 we get
⇒ a3 = 1728
∴ a = 12.
From 1 we get
⇒ 
⇒ a + ar + ar2 = 65r …(3)
Substituting a = 12 in 3 we get
⇒ 12 + 12r + 12r2 = 38r
⇒ 12r2 – 26r + 12 = 0…(4)
Dividing (4) by 2 we get
⇒ 6r2 – 13r + 6 = 0
⇒ 6r2 – 12r – r + 6 = 0
⇒ 6r(r – 2) – 1(r – 2) = 0
∴ r = 2 or r = 1/2
∴ Now the equation will be
⇒ 
⇒ 6,12,24 or 24,12,6.
∴ The three numbers are 6,12,24.
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