Question

若X的平方-4分之4X=X+2分之a-X-2分子b,则a平方+b平方的值

Answer 1

4x/(x^2-4)=A/(x+2)-B/(x+2)

=[A(x-2)-B(x+2)]/(x^2-4)

=[(A-B)x-(2A+2B)]/(x^2-4)(两边恒等)

则A-B=4

-(2A+2B)=0

解得

A=2

B=-2

则A^2+B^2=8