Question

Average of a b c is p and ab+bc+ca=3 what is the average of a^2 b^2 c^2

Answer 1

Answer:

The average of a² + b² + c² = p² -2.

Step-by-step explanation:

a² + b² + c²  = (a+b+c)² - 2( a×b  +  b×c + c×a)

(a²+ b² + c²)÷ 3 =  ( ( a+b+c)² - 2(a×b + b×c + c×a)) ÷ 3 , let it be equation 1

given average of a, b,c =p

that is (a+b+c)÷3= p

(a+b+c)= 3p

and  ab + bc + ca = 3

Substituting the values of a+b+c and ab + bc +ca in equation 1

average is given by

(3p² - 2×3)÷3=  p²-2

The average of a² + b² + c² = p² -2.