**Question 01**

**If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a ^{2}, b^{2}, c^{2} is:**

**Given**: Mean of a, b, c = M;

ab +bc + ca = 0

Or, (a + b + c)/3 = M

a + b + c = 3M

Squaring both sides, (a + b + c)^{2} = (3M)^{2}

a^{2} + b^{2} + c^{2} + 2 (ab + bc + ca) = 9M^{2} ** Formula used** **[(a + b + c) ^{2} = a^{2} + b^{2} + c^{2} + 2 (ab + bc + ca)]**

a^{2} + b^{2} + c^{2 } + 2. 0 = 9M^{2} (ab + bc + ca = 0)

(a^{2} + b^{2} + c^{2} )/3 = 3M^{2} = required mean

**Ans. Required mean is 3M ^{2}**