已知实数x.y满足（x2+y2）（x2+y2-1）=2,求x2+y2的值

已知实数x.y满足（x2+y2）（x2+y2-1）=2,求x2+y2的值

可设x²+y²=t.则t(t-1)=2.===>t²-t-2=0.===>(t-2)(t+1)=0.===>t=2.即x²+y²=2.

可设x²+y²=t.则t(t-1)=2.===>t²-t-2=0.===>(t-2)(t+1)=0.===>t-2=0或t+1=0===>t1=2，t2=-1.即x²+y²=2或-1.