Question

If the mean if x and 1/x is M then the mean of x square and 1 by x square is K M square minus 1 then find the value of K

Answer 1

Answer:K=√2 or -√2

Step-by-step explanation:

x+1/x/2=M---> 1

x^2+1/x^2=(KM)^2-1----->2

From 1 we get,

x^2+1/2x=M

x^4+1+2x^2/4x^2=M^2

From 2 we get,

x^4+1/2x^2=(KM)^2-1

x^4+1/2x^2+1=(KM)^2

x^4+2x^2+1/2x^2=(KM)^2

x^4+2x^2+1/2x^2=K^2M^2

x^4+2x^2+1/2x^2=K^2(x^4+1+2x^2/4x^2)

1/2x^2=K^2/4x^2

1=K^2/2

K^2=2

K=√2 or K= -√2