Question

已知x^2+1/x=根号5,求x^4+x^2+1/x^4-x^2+1的值

Answer 1

已知x^2+1/x²=根号5,
x^4+x^2+1/x^4-x^2+1的值
=（x²+1+1/x²）/(x²-1+1/x²)
=(√5+1)/(√5-1)
=(√5+1)²/(5-1)
=(5+1+2√5)/4
=(3+√5)/2;