若\(\displaystyle x=\frac{1}{2}(3^{\frac{1}{100}}-3^{\frac{-1}{100}})\)，求\((\sqrt{1+x^2}+x)^{100}\)之值

sqrt(1 + x^2) = [3^(1/100) + 3^(-1/100)] / 2

所求 = { 1 / [sqrt(1 + x^2) - x] }^100 = 3

感謝前輩熱心回復!!!