Question

find the two numbers whose arithmetic mean is 5/3 ,which are reciprocal to each other.
​

Answer 1

Answer:

3 and 1/3

Step-by-step explanation:

let the numbers be 1/x and x

ATQ,

x+1/x /2=5/3

x^2+1/x=10/3

3x^2+3=10x

3x^2-10x+3=0

3x^2-9x-x+3=0

3x(x-3)-1(x-3)=0

(3x-1)(x-3)=0

therefore x=3 and x=1/3

Answer 2

Answer:

3 and 1/3

Step-by-step explanation:

Let one of the number be x.

Then the other one will be 1/x.

Mean of both the numbers

= (x+1/x)/2=5/3

=x+1/x=10/3

=(x^2+1)/x=10/3

=3x^2+3=10x

=3x^2-10x+3=0

=(3x-1)(x-3)=0

Therefore,

x=3 or 1/3

This gives us the two numbers 3 and 1/3.

Hopefully I think this will help you.