Question

If the mean of a,b,c,d is M and ab+bc+ca=0 , the mean of a^2,b^2.c^2is KM^2 then k is

Answer 1

Step-by-step explanation:

Correction :-

observations are a,b,c

Given :-

The mean of a,b,c is M and ab+bc+ca=0

The mean of a²,b² and c² is KM²

To find :-

Find the value of K ?

Solution :-

Given that

Given observations are a,b,c

We know that

Mean = Sum of all observations/ Number of all observations

=>Mean a,b,c = (a+b+c)/3

According to the given problem

The mean of a,b,c = M

=> (a+b+c)/3 = M

=> a+b+c = 3M -----------(1)

On squaring both sides then

=> (a+b+c)² = (3M)²

=> a²+b²+c²+2ab+2bc+2ca = 9M²

=> a²+b²+c²+2(ab+bc+ca) = 9M²

Given that

ab+bc+ca = 0

So, On Substituting this value in it

a²+b²+c²+2(0) = 9M²

=> a²+b²+c²+0 = 9M²

=>a²+b²+c² = 9M²----------(2)

And

Mean of a²,b²,c² = (a²+b²+c²) /3

=> Mean = 9M²/3 (from (2))

=> Mean = 3M²

According to the given problem

The mean of a²,b²,c² = KM²

=> 3 M² = KM²

On Comparing both sides then

K = 3

Answer:-

The value of K for the given problem is 3

Used formulae:-

Mean = Sum of all observations/ Number of all observations

• (a+b+c)² = a²+b²+c²+2ab+2bc+2ca