Question

已知X/X²-X+1=1/5,求X²/X4次方+X²+1的值

Answer 1

x/(x²-x+1)=1/5

1/(x -1 +1/x)=1/5 /分子分母同除以x

x -1 +1/x=5

x+ 1/x=6

x²/(x⁴+x²+1)

=1/(x² +1 +1/x²) /分子分母同除以x²

=1/[(x+1/x)² -1] /分母配方

=1/(6²-1)

=1/35