divide 36 into 4 parts so that it is in AP such that the ratio of product of extremes to product of means is 45:77.
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Answers
Answered by
15
Step-by-step explanation:
let
the number of four parts are
sum of the number
a-3d+a-d+a+d+a+3d=36
4a=36
a=36/4=9
given that
product of extreme to product of means
so,
a+3d*a-3d/a-d*a+d=45/77
a^2-9d^2/a^2-d^2=45/77
77a^2-693d^2=45a^2-45d^2
now
putting value of a
77*81-693d^2=45*81-45d^2
d^2=4
d=√4=2
so Ap
9, 11, 13 ,15,17
I hope it will be helpful
Answered by
7
Step-by-step explanation:
in AP : a,a+d,a+2d,a+3d
total of AP = 36
a+a+d+a+2d+a+3d = 36
4a+6d = 36
2a+3d = 18
a = (18-3d)/2
Product Ratio of extremes = 45:77
a(a+3d)/(a+d)(a+2d) = 45/77
77a^2+231ad =45 (a^2+2d^2+3ad)
77a^2 + 231ad = 45a^2 + 90d^2 + 135ad
32a^2 + 96ad - 90d^2 = 0
16a^2 + 48ad - 45d^2 = 0
(4a+6d)^2 = 81d^2
36^2 = 81d^2
4*4 = d^2
d = 4
a = 18-3d/2 = 18-12/2 = 3
a= 3
d= 4
so A.P = 3,7,11,15
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