已知有理数xy满足(x²+y²)(x²+y²-1)-6=0,则x²+y²的值为

问题描述:

已知有理数xy满足(x²+y²)(x²+y²-1)-6=0,则x²+y²的值为

设t=x²+y² t≥0则
(x²+y²)(x²+y²-1)-6=0
t(t-1)-6=0
t²-t-6=0
(t-3)(t+2)=0
t-3=0
t=3
所以x²+y²的值为3