∵a²-5a+1=0 ∴a²=5a-1 a4=（5a-1）²=25a²-10a+1=25x（5a-1）-10a+1=115a-24
a²/（a4+a²+1）=（5a-1）/（115a-24 +5a-1 +1）=（5a-1）/（120a-24）=1/24因式分解（x+y)(x+y+2xy)+x的平方y的平方-1（x+y)(x+y+2xy)+x²y²-1=x²+2xy+y²+2x²y+2xy²+x²y²-1=（x²+2x²y+x²y²）+（2xy+2xy²）+（y²-1）=x²（y+1）²+2xy（y+1）+（y+1）（y-1）=（y+1）（xy²+x²+2xy+y-1）=（y+1）{（xy²+xy）+（xy+y）+（x²-1）}=（y+1）（x+1）（xy+y+x-1）