x²=1/4[5^(2/n)-2+5^(-2/n)]
1+x²=1+1/4[5^(2/n)-2+5^(-2/n)]=1/4[4+5^(2/n)-2+5^(-2/n)]
=1/4[5^(2/n)+2+5^(-2/n)]
=[1/2(5^1/n+5^-1/n)]²
显然5^1/n+5^-1/n>0
所以根号1+x^2=1/2(5^1/n+5^-1/n)
所以x+根号1+x^2=1/2(5^1/n-5^-1/n)+1/2(5^1/n+5^-1/n)
=5^(1/n)
所以原式=]5^(1/n)]^n=5