已知（x-1)³分之x²+2=（x-1)分之A+（x-1)²分之B+(x-1)³分之C,求A、B、C的值

Question

已知（x-1)³分之x²+2=（x-1)分之A+（x-1)²分之B+(x-1)³分之C,求A、B、C的值

Answer 1

（x-1)³分之x²+2
=（x-1)分之A+（x-1)²分之B+(x-1)³分之C,求A、B、C的值
=(A(x-1)²+B(x-1)+C)/(x-1)³;
∴Ax²+(B-2A)x+A-B+C=x²+2;
A=1;
B-2A=0;
B=2;
A-B+C=2;
C=2+2-1=3;
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