数学题!已知：x的平方=x+1 求：x的5次方-5x+2

题目

数学题!已知：x的平方=x+1 求：x的5次方-5x+2
要有过程和结果

答案

x5-5x+2
=x(x4-4)-x+2
=x(x2-2)(x2+2)-x+2 代入x2=x+1
=x(x+1-2)(x+1+2)-x+2
=x(x-1)(x+3)-x+2
=(x2-x)(x+3)-x+2 代入x2=x+1
=(x+1-x)(x+3)-x+2
=x+3-x+2
=3+2
=5