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Question -

If a2 + b2 + c2 = 20 and a + b + c = 0, find ab + bc + ca.



Answer -

a2 +b2 + c2 = 20, a + b + c = 0
(a + b+ c)2 = 0
a2 + b2 + c2 + 2(ab + bc + ca)= 0
 20 + 2(ab + be + ca) = 0
 2(ab + bc + ca) = -20
ab + bc + ca = 
202 =-10

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