three numbers are in continued proportion, whose mean proportiin is 12 and sum of remaining two numbers is 26,then find the numbers
Answers
The three numbers are
12and26= 12-26
12and26=12
12and26=12diveded into three parts=?
12divided into three parts =3÷12=4
=thus the number of three parts = 8 , 12 , 18
that's it....
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Answer:
The required numbers are 8, 12 and 18 or 18, 12 and 8
Step by step explanation:
Let a, b and c be the three numbers in continued proportion.
Then b = 12 and a + c = 26 ...(1)
b² = ac
=> 12² = ac
=> ac = 144
=> a = 144/c (2)
Substituting a = 144/c from (2) in a + c in (1)
=> 144/c + c = 26
=> 144 + c² = 26c
=> c² - 18c + 8c + 144 = 0
=> c(c - 18) + 8(c - 18) = 0
=> (c - 18) (c + 8) = 0
=> c - 18 = 0
=> c = 18
OR
=> c - 8 = 0
=> c = 8
Now, a + c = 26
=> a = 26 - 18
=> a = 26 - 8
OR, a + c = 26
=> a = 26 - 8
=> a = 18
The required number 8, 12 and 18 or 18, 12 and 8.
Hope it helps :)