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InterviewSolution
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If the average of a, b, c is M and ab + bc + ca = 0, then the average of a2 , b2 , c2 is (a) M2 (b) 3M2 (c) 6M2 (d) 9M2 |
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Answer» Answer is: (b) 3M2 Given, \(\frac{a+b+c}{3}=M\) ⇒ a + b + c = 3M Now, (a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca) ⇒ (3M)2 = a2 + b2 + c2 + 0 ⇒ a2 + b2 + c2 = 9M2 Average of a2 + b2 + c2 = \(\frac{a^2 + b^2 + c^2}{3}=\frac{9M^2}{3}=3M^2\) |
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