(1/a+1/b+1/c)^2=1/a^2+1/b^2+1/c^2+2/ab+2/ac+2/bc=(1/a^2+1/b^2+1/c^2)+2(1/ab+1/ac+1/bc)=(1/a^2+1/b^2+1/c^2)+2[(a+b+c)/abc]=(-4)^2=16我们知道 a+b+c=0所以1/a^2+1/b^2+1/c^2=16
