Answer:
2, 1/2
Step-by-step explanation:
Arithmetic mean of two numbers is given as
[tex]n=\frac{a+b}{2}[/tex]
Here a=x and b=1/x
[tex]n=\frac{x+1/x}{2}[/tex]
[tex]\frac{5}{4} =\frac{x^{2}+1}{2x}[/tex]
[tex]\frac{5}{2}x=x^{2} +1\\ x^{2}-\frac{5}{2}x+1=0[/tex]
[tex]x=2, \frac{1}{2}[/tex]
Hence the numbers are 1/2 and 2.
If x is any real number, then the reciprocal of this number will be 1/x. For example, the reciprocal of 5 is 1 divided by 8, i.e. 1/5.
Given, one number is reciprocal to another.
So if we choose the first number to be x , the the other number becomes its reciprocal i.e. 1/x.
Now, it is given that the arithmetic mean of these two numbers is 5/4.
So using formula for arithmetic mean ,
Mean = Sum of Observations / No. of observations
[tex]\frac{5}{4} =\frac{x+\frac{1}{x}}{2} \\\frac{5*2}{4}= \frac{x^{2} +1}{x} \\\frac{5}{2} =\frac{x^{2}+1}{x} \\[/tex]
On cross Multiplication and Factorization, we get:
[tex]5x=2x^{2}+2\\2x^{2} -5x+2=0\\2x^{2} -4x-x+2=0\\2x(x-2)-1(x-2)=0\\(2x-1)(x-2)=0\\2x-1=0 , x=1/2\\x-2=0 , x=2[/tex]
So , when x=1/2 , then 1/x=2
and when x=1/2 , then x=2
Hence, the numbers are 2 and 1/2 .
Learn more about reciprocals at :
https://brainly.com/question/2534506
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