If is a root of the equation x2+x+1=0 and k=1n ( k+ 1 k )2=20, then n is equal to .
11
x2+x+1=0 = or 2, so 3=1 and 1+ + 2=0
( k+ 1 k )2= 2k+ -2k+2
If k is a multiple of 3: 2k= -2k=1 term =1+1+2=4
Otherwise: 2k+ -2k= 2k+ k=-1 term =-1+2=1
every block of three terms (k=3r-2, 3r-1, 3r) gives 1+1+4=6
k=1 to 9: 3 6=18; k=10: 18+1=19; k=11: 19+1=20
n=11
Answer: 11
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