已知X=根号2+1,求代数式(X-1/X)^2+2(X-1/X)+1的值
问题描述:
已知X=根号2+1,求代数式(X-1/X)^2+2(X-1/X)+1的值
答
(X-1/X)^2+2(X-1/X)+1
=(x-1/x+1)^2
=(√2+1-1/(√2+1)+1)^2
=(√2+1-(√2-1)/(2-1)+1)^2
=(√2+1-√2+1+1)^2
=3^2
=9