Question

Three number are in continued proportion,whose mean proportional us 12 and the sum of the remeanining two numbers is 26,the find these numbers.​

Answer 1

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Given :-

• Three numbers a, b, c are in continued proportion whose mean proportion is 12 and sum of other two numbers (a and c) be 26.

To find :-

• The numbers a, b, c.

Solution:-

Let the numbers be a, b, c so that they are in continued proportion.

So b is called mean proportion between 'a' and 'c'.

Since, mean proportion is 12

=> b = 12

Now, according to statement,

a + c = 26

=> c = 26 - a ....(1)

Since a, b, c are in continued proportion,

=> b² = ac

=> 12² = a × (26 - a) [using (1) and b = 12]

=> 144 = 26a - a²

=> a² - 26a + 144 = 0

=> a² - 18a - 8a + 144 = 0

=> a(a - 18) - 8(a - 18) = 0

=> (a - 18)(a - 8) = 0

=> a = 18 or 8

So, when a = 8 => c = 18

and when a = 18 => c = 8

So numbers are 8, 12 and 18 or 18, 12 and 8.

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