已知f（x-1/x）=x方+1/x方,求f（x-1）!

已知f（x-1/x）=x方+1/x方,求f（x-1）!
已知f（x-1/x）=x方+1/x方,求f（x-1）!

已知f（x-1/x）=x方+1/x方,求f（x-1）!
a=x-1/x
a²=x²-2+1/x²
x²+1/x²=a²+2
所以f(a)=a²+2
所以f(x-1)=(x-1)²+2=x²-2x+3

f(x-1/x)=x^2+1/x^2
=(x-1/x)^2+2
f(x)=x^2+2
f(x-1)=(x-1)^2+2
=x^2-2x+1+2
=x^2-2x+3

f（x-1/x）=x方+1/x-2+2=（x-1/x）^2+2
f(x)=x^2-2
f(x-1)=x^2-2x-1

f（x-1/x）=x²+1/x²=x²-2+1/x²+2=(x-1/x)²+2
令t=x-1/x，则f(t)=t²+2
所以f(x-1)=(x-1)²+2