JIPMAT 2022 (QA) - If the mean of a, b, and c is M; ab + bc + ca = 0; and the mean of a^2, b^2 and c^2 is KM^2, then K is equal to | PYQs + Solutions

JIPMAT 2022

Arithmetic

Averages

Medium

If the mean of $a$ , $b$ , and $c$ is $M$ ; $ab + bc + ca = 0$ ; and the mean of $a^2$ , $b^2$ and $c^2$ is $KM^2$ , then $K$ is equal to

Correct Option: 1

From mean of

a

b

, and

c

\frac{a + b + c}{3} = M

a + b + c = 3M

...(1)

Given:

ab + bc + ca = 0

...(2)

Mean of squares:

\frac{a^2 + b^2 + c^2}{3} = KM^2

a^2 + b^2 + c^2 = 3KM^2

...(3)

From (1): squaring both sides

\newline

(a + b + c)^2 = 9M^2

\newline

a^2 + b^2 + c^2 + 2(ab + bc + ca) = 9M^2

From (2):

\newline

a^2 + b^2 + c^2 = 9M^2

From (3):

\newline

3KM^2 = 9M^2

\newline

\boxed{K = 3}

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