已知(u²+v²)(1-u²-v²)+6=0,求u²+v²的值,快快快如题,求学霸帮忙

已知(u²+v²)(1-u²-v²)+6=0,求u²+v²的值,快快快如题,求学霸帮忙
已知(u²+v²)(1-u²-v²)+6=0,求u²+v²的值,快快快
如题,求学霸帮忙

已知(u²+v²)(1-u²-v²)+6=0,求u²+v²的值,快快快如题,求学霸帮忙
假设u²+v²=x
则x(1-x)+6=0
(x+2)(x-3)=0
x1=-2,x2=3
u²+v²>=0
x=3

(u²+v²)(1-u²-v²)+6=0
(u²+v²)(u²+v²-1)-6=0
(u²+v²)²-(u²+v²)-6=0
(u²+v²+2)(u²+v²-3)=0
因为(u²+v²)≥0
所以
(u²+v²)=3

u²+v²看成X且X≥0
x(1-x)+6=0
x^2-x-6=0
x=3,或x=-2(舍去)