已知实数a,b,c满足abc=-1,a
a/(a²-3a-1)
=1/ (a-3-1/a)
=1/(a-(a+b+c-1)+abc/a)
=1/(1-b-c+bc)
=1/(b-1)(c-1)
a/(a²-3a-1)+b/(b²-3b-1)+c/(c²-3c-1)=4/9
1/(b-1)(c-1)+1/(c-1)(a-1)+1/(a-1)(b-1)=4/9
(a-1+b-1+c-1)/(a-1)(b-1)(c-1)=4/9
(a+b+c-3)/(a-1)(b-1)(c-1)=4/9
1/(a-1)(b-1)(c-1)=4/9
(a-1)(b-1)(c-1)=9/4
abc-ab-bc-ca+a+b+c-1=9/4
ab+bc+c...全部
a/(a²-3a-1)
=1/ (a-3-1/a)
=1/(a-(a+b+c-1)+abc/a)
=1/(1-b-c+bc)
=1/(b-1)(c-1)
a/(a²-3a-1)+b/(b²-3b-1)+c/(c²-3c-1)=4/9
1/(b-1)(c-1)+1/(c-1)(a-1)+1/(a-1)(b-1)=4/9
(a-1+b-1+c-1)/(a-1)(b-1)(c-1)=4/9
(a+b+c-3)/(a-1)(b-1)(c-1)=4/9
1/(a-1)(b-1)(c-1)=4/9
(a-1)(b-1)(c-1)=9/4
abc-ab-bc-ca+a+b+c-1=9/4
ab+bc+ca
= abc+a+b+c-1-9/4
= -1+4-1-9/4
= -1/4
a²+b²+c²
= (a+b+c)²-2(ab+bc+ca)
= 4²-2*(-1/4)
= 33/16。
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