若a^2+b^2=1,b^2+c^2=2,a^2+c^2=3,a^4+b^4+c^4+2a^2b^2+2a^2c^2+2

由原式得：a^2+b^2+2c^2=5,则c^2=2,a^4+b^4+c^4+2a^2b^2+2a^2c^2+2b^2c^2=(a^2+b^2)+2c^2(a^2+b^2)+c^4=1+2c^2+c^4=(c^2+1)^2=3^2=9