y=[x+(1+x^2)^1/2]^1/3+[x-(1+x^2)^1/2]^1/3
等式右边分子分母同乘以[x-(1+x^2)^1/2]^1/3得:
y=[([x-(1+x^2)^1/2]^1/3)^2 -1]/([x-(1+x^2)^1/2]^1/3)
=[x-(1+x^2)^1/2]^1/3 - 1/([x-(1+x^2)^1/2]^1/3)
等式两边同时3次方,得:
y^3 = x-(1+x^2)^1/2 -3{[x+(1+x^2)^1/2]^1/3+[x-(1+x^2)^1/2]^1/3} - 1/[x-(1+x^2)^1/2]
y^3 +3y = x-(1+x^2)^1/2- 1/[x-(1+x^2)^1/2]
等式右边1/[x-(1+x^2)^1/2]分子分母同乘以x+(1+x^2)^1/2
y^3 +3y =x-(1+x^2)^1/2 + [x+(1+x^2)^1/2]
y^3 +3y =2x
x = 1/2 (y^3 +3y)