if the arithmetic mean of two number is 4.5 and their harmonic mean is 4 then find numbers
Answers
let numbers be a and b, then
Arithmetic Mean :
a+b / 2 = 4.5 or a+b = 9----I
Harmonic Mean : 2ab / (a+b) = 4
or ab=18 ----II
We have the sum and product from I and II, we need to find the a and b.
We will do it using Algebraic identity, (a+b)^{2} - (a-b)^{2} = 4ab
9^{2} - (a-b)^{2} = 4(18)
a-b=3 ----III
Solve I and III for value of a and b
we get a=6 and b=3
Answer:
The two numbers will be 3 and 6.
Step-by-step explanation:
We have given the arithmetic mean = 4.5
The harmonic mean of two numbers = 4
Consider that 'a' and 'b' are the two numbers.
The arithmetic mean of a and b
.................(1)
Harmonic mean of two numbers is the reciprocal of the arithmetic mean of reciprocals of those two numbers.
The harmonic mean of a and b
Substitute the value of 'b' from equation (1);
Substitute the value of a in equation (1), we get;
For
For a=6, b = 9-6 = 3
Therefore, the two numbers will be 3 and 6.