please answer by solving

3 number are in continued proportion the sum of second and third is 16 and the product of all is 8000 find the sum of all three numbers

# please answer by solving

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Answer:let the there numbers be

a,b,c

As they are in continued

Proportion

b

2

=ac

mean is 12

∴b=12

So, 12

2

=ac

144=ac

c=144/a

Sum of two number is

a+c=26

a+

a

144

=26

Solving,

=a

2

+144−26a=0

=a

2

−18a−8a+144=0

=a(a−18)−8(a−18)=0

=(a−18)(a−8)=0

∴a=18 or a=8

c=8 c=18

∴ The numbers are :-

8,12,18 or 18,12,8