Question

已知(m²+n²)(m²+1+n²)=6,求m²+n²的值

Answer 1

(m²+n²)(m²+1+n²)=6

(m²+n²)(m²+n²+1)=6

（m^2+n^2）^2+(m^2+n^2)-6=.0

(m^2+n^2+3)(m^2+n^2-2)=0

所以,m^2+n^2+3=0 m^2+n^2-2=0

m²+n²≥0

m^2+n^2=-3(舍去） m^2+n^2=2