We are going to find the condition necessary for xi2 = ( xi)2. (As we saw in cla

Question

We are going to find the condition necessary for xi2 = ( xi)2. (As we saw in class in general xi2 ( xi)2. But under some very specific conditions, xi2 = ( xi)2 might be true.) For n=2, write explicitly (without using the symbol ) what xi2 is. For n=2, write explicitly ( xi)2. Then what has to be true of x1 and x2 for xi2 = ( xi)2 when n=2 ? For n=3, write explicitly xi2 and ( xi)2 Then what has to be true of x1, x2 and x3 for xi2 = ( xi)2 when n=3 ? For any n, show that ( xi)2 = xixj (A bit hard, some hand waving or an intuitive explanation is acceptable, in particular using the previous answers.)

Explanation / Answer

a)X12 +X22

B)(X1+X2)2

C)(X1+X2)2=X12 +X22

SO X1 OR X2 HAS TO BE ZERO

D)X12 +X22 +X32 AND (X1+X2+X3)2

E)2(X1*X2+X2*X3+X1*X3)=0 SO SUMM OF PAIRS IS ZERO

F)IT IS A IDENTITY WHICH CAN BE FOUND BY TAKING (X1+X2) AS ONE TERM THEN APPLYING SWUARE RULE ON (X1+X2) AND X3 DURING SQUARING AND THEN BREAKING THIS SQUARE AT LATER STAGES

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