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If the mean of a, b, c is M1 and a^2, b^2, c^2 is M2, then one mean of ab, bc, ca is

Given \(a + b + c = 3M_1\) and \(a^2 + b^2 + c^2 = 3M_2\), we have \(ab + bc + ca = \frac{(a+b+c)^2 - (a^2+b^2+c^2)}{2} = \frac{9M_1^2 - 3M_2}{2}\). Dividing by 3 gives the…

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If the mean of a, b, c is M1 and a^2, b^2, c^2 is M2, then one mean of ab, bc, ca is

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Correct answer C

Given a+b+c=3M1a + b + c = 3M_1 and a2+b2+c2=3M2a^2 + b^2 + c^2 = 3M_2, we have ab+bc+ca=(a+b+c)2−(a2+b2+c2)2=9M12−3M22ab + bc + ca = \frac{(a+b+c)^2 - (a^2+b^2+c^2)}{2} = \frac{9M_1^2 - 3M_2}{2}. Dividing by 3 gives the mean 3M12−M22\frac{3M_1^2 - M_2}{2}.

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  • Rajasthan Clerk Grade 2

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