Question

a=根号5-1/2求a的5次方+a的4次方-2a的3次方-a的2次方-a+2/a的3次方-a的值

Answer 1

a = (√5-1)/2 ,

2a = √5-1 ,

2a+1 = √5 ,

(2a+1)² = (√5)² ,

4a²+4a+1 = 5 ,

4a²+4a-4 = 0 ,

a²+a-1 = 0 ,

(a^5+a^4-2a^3-a^2-a+2)/(a^3-a)

= [a^3(a²+a-1)-a(a²+a-1)-2(a-1)]/[a(a+1)(a-1)]

= -2(a-1)/[(a²+a)(a-1)]

= -2/[(a²+a-1)+1]

= -2/1

= -2