Question

1.已知x-1/x=2,求x²/x四次方-x²+1 2.已知已知b+1/c=1,c+1/a=1,求a

Answer 1

x-1/x=2

（x-1/x）²=2²

x²-2+1/x²=4

x²+1/x²=6

x²/x四次方-x²+1

=1/(x²-1+1/x²)

=1/(6-1)

=1/5

由b+1/c=1,得：b=1-1/c=(c-1)/c,则1/b=c/(c-1),

由c+1/a=1,得：1/a=1-c,则a=1/(1-c),

所以

(ab+1)/b

=a+1/b

=1/(1-c)+c/(c-1)

=1/(1-c)-c/(1-c)

=(1-c)/(1-c)

=1