Question

the arithmetic mean, geometric mean and median of six positive numbers a, a, b, b, c, c where a<b<c are 7/3,2,2respectively. then what is the sum of the squares of all the six numbers

Answer 1

Answer:

42

Step-by-step explanation:

Hi,

Given 6 positive numbers are a, a, b, b, c, c

Arithmetic mean of given 6 numbers is (a + a + b + b + c+ c)/6

= (a + b + c)/3 = 7/3

⇒a + b + c = 7

Median of the given 6 positive numbers is (b + b)/2 = 2

⇒ b = 2

⇒ a + c = 5-----(*)

Geometric mean of given 6 numbers is

($\sqrt[a.a.b.b.c.c]{6}$) = 2

⇒ ∛abc = 2

⇒ abc = 8

⇒ ac = 4

Using (*) in above, we get a = 1 and c = 4.

Hence the given 6 positive numbers area

1, 1, 2, 2, 4, 4.

Sum of squares of all the six numbers are

1 + 1 + 4 + 4 + 16 + 16

= 42

Hope, it helped !