设m=x-1 n=y+3
则m^(1/3)+n^(1/3)=2 (1)
m+n=26 (2)
(1)^3 得 m+n+3(mn)^(1/3)*[m^(1/3)+n^(1/3)]=8
(1)(2)代入上式 26+3*2*(mn)^(1/3)=8
(mn)^(1/3)=-3
再立方得 mn=-27 (3)
(2)(3)联立 m,n 是方程x²-26x-27=0的两根
(x-27)(x+1)=0
解得x=27或-1
所以m=27 n=-1时 x-1=27 x=28 y+3=-1 y=-4
m=-1 n=27时 x-1=-1 x=0 y+3=27 y=24
故x=28 y=-4
或x=0 y=24