x2-x-1=0求x4+2x+1/x5的值我解出来了，看正解：由题意知：x2-x-1=0所以：x+1=x2x4+2x+1=x4+x+x+1=x4+x+(x+1)=x4+x+x2=x(x3+1+x)=x(x3+x2)=x[x2(x+1)]=x(x2x2)=x5原式=x5/x5=1

Question

x2-x-1=0 求x4+2x+1/x5的值
我解出来了，看正解：
由题意知：x2-x-1=0 所以：x+1=x2
x4+2x+1
=x4+x+x+1
=x4+x+(x+1)
=x4+x+x2
=x(x3+1+x)
=x(x3+x2)
=x[x2(x+1)]
=x(x2 x2)=x5
原式=x5/x5=1

Answer 1

经计算,该方程有两个
x1 = (√5 - 1) / 2
x2 = (-√5 - 1) / 2
当 x1 = (√5 - 1) / 2 时,
原式= {[(√5 - 1) / 2] ^4 + 2 (√5 - 1) / 2 + 1 } / [ (√5 - 1) / 2 ] ^5
= { [(√5)² - 2√5 + 1)] [(√5)² -2√5 + 1] + √5 } / [(√5)² - 2√5 + 1)] [(√5)² -2√5 + 1](√5-1) / 2
= .