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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