Question

Mean of x ,1/x is M, Find the mean of x³,1/x³.​

Answer 1

Answer:

Required mean of x^3 and 1 / x^3 is 4M^3 - 3M.

Step-by-step explanation:

It is given that the mean of x and 1 / x is M.

From the properties of mean : -

• Mean = ( sum of observations ) / ( number of observations )

Here,

Observations : x and 1 / x

Number of observations : 2

Mean of observations : M

Thus,

= > M = ( x + 1 / x ) / 2

= > 2 M = x + 1 / x

Cube on both sides : -

= > ( 2 M )^3 = ( x + 1 / x )^3

= > 8 M^3 = x^3 + 1 / x^3 + 3( x × 1 / x )( x + 1 / x )

= > 8 M^3 = x^3 + 1 / x^3 + 3( 1 )( 2M )         { from above, x + 1 / x = 2M }

= > 8 M^3 = x^3 + 1 / x^3 + 6M

= > 8 M^3 - 6M = x^3 + 1 / x^3

= > 2[ 4M^3 - 3M ] = x^3 + 1 / x^3

Then,

= > Mean of x^3 and 1 / x^3 = ( x^3 + 1 / x^3 ) / 2

From above, substituting the value of x^3 + 1 / x^3

= > Mean of x^3 + 1 / x^3 = [ 2{ 4M^3 - 3M } ] / 2

= > Mean of x^3 and 1 / x^3 = 2M^3 - 3M

Hence the required mean of x^3 and 1 / x^3 is 4M^3 - 3M.

Answer 2

Answer:

the required mean of x^3 and 1 / x^3 is 4M^3 - 3M.