Three numbers are in continued proportion, whose mean proportional is 12 and the sum of the remaining two numbers is 26, then find these numbers.
Answers
Step 1 : Assume the number and follow given instruction
Let the there numbers be a,b,c
As they are in continued proportion
b^ 2=ac
Given that mean proportional is 12
∴b=12
So, 12 ^2 =ac
144=ac
c= a/144
The sum of the remaining two numbers is 26
a+c=26
a+ a/144
=26
Step 2 : Simplify using factorization
On solving we get,
⇒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 or c = 18
Hence , The numbers are 8,12,18 or 18,12,8
Answer:
Step 1 : Assume the number and follow given instruction
Let the there numbers be a,b,c
As they are in continued proportion
b
2
=ac
Given that mean proportional is 12
∴b=12
So, 12
2
=ac
144=ac
c=
a
144
The sum of the remaining two numbers is 26
a+c=26
a+
a
144
=26
Step 2 : Simplify using factorization
On solving we get,
⇒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 or c = 18
Hence , The numbers are 8,12,18 or 18,12