Average Practice Test 2

Question : 40 of 40

Marks: +1, -0

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

a^2, b^2, c^2

is:

Solution:

Here,

{a+b+c}/3=M

∴ a + b + c = 3M
Now,

(a + b + c)^2

= a^2 + b^2 + c^2 + 2(ab + bc + ca)

⇒ (3M)^2 = a^2 + b^2 + c^2 + 2 × 0

(∵ ab + bc + ca = 0)

⇒ a^2 + b^2 + c^2 = 9M^2

⇒ {a^2 + b^2 + c^2}/3 = {9M^2}/3=3M^2

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