Question

已知x=根号2 -1，求（x^2+1/x^2)^2+4(x^2+1/x^2）+4

Answer 1

x=根号2 -1，
x+1=根号2
平方，得
x²＋2x＋1=2
x²＋2x-1=0
x+2-1/x=0
x-1/x=-2
平方，得
x²-2+1/x²=4
x²＋1/x²=6
所以
（x^2+1/x^2)^2+4(x^2+1/x^2）+4
=(x²＋1/x² ＋2)²
=(6+2)²
=64

Answer 2

答：
x=√2-1
1/x=1/(√2-1)=√2+1
x+1/x=√2-1+√2+1=2√2

(x^2+1/x^2)^2+4(x^2+1/x^2)+4
=(x^2+1/x^2+2)^2
=(x+1/x)^4
=(2√2)^4
=64