已知X/X²-X+1=1/5,求X²/X4次方+X²+1的值

题目

已知X/X²-X+1=1/5,求X²/X4次方+X²+1的值

答案

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