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If the mean of a, b, c, is M and ab + bc + ca = 0, then the mean of a2, b2, c2 is –
- A. M2
- B. 3M2
- C. 6M2
- D. 9M2
Answer: Option B
Here is complete explanation of If the mean of a b c is M and ab….
Solution(By ExamCraze Team)
We have :
$$frac{a + b + c}{3}$$ = M
or (a + b + c) = 3M
Now, (a + b + c)2 = (3M)2 = 9M2
⇔ a2 + b2 + c2 + 2 (ab + bc + ca) = 9M2
⇔ a2 + b2 + c2 = 9M2
[$$because $$ (ab + bc + ca) = 0]
∴ Required mean
$$eqalign{
& = left( {frac{{{a^2} + {b^2} + {c^2}}}{3}} right) cr
& = frac{{9{M^2}}}{3} cr
& = 3{M^2} cr} $$
