Question

已知x=根号2+1,求(x+x分之1）的二次方 减去 2乘（x+x分之1）+1的值

Answer 1

(x-1)^2=跟好2的平方=2

x²-2x+1=2

x²+1=2x+2

(x+1/x)²-2(x+1/x)+1

=(x+1/x-1)²

=[(x²+1-x)/x]²

=[(2x+2-x)/x]²

=[(x+2)/x]²

=(1-2/x)²

2/x=2(根号2-1)/(根号2+1)(根号2-1)=2根号2-2

所以原式=(1-2根号2+2)²

=9-12根号2+8

=17-12根号2