please answer by solving
3 number are in continued proportion the sum of second and third is 16 and the product of all is 800

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 ​

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  1. 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

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