若x^2+4y^2+2x+4y+2=0,求5x^2+16y^2的算术平方根.

若x^2+4y^2+2x+4y+2=0,求5x^2+16y^2的算术平方根.
若x^2+4y^2+2x+4y+2=0,求5x^2+16y^2的算术平方根.

若x^2+4y^2+2x+4y+2=0,求5x^2+16y^2的算术平方根.
x^2+4y^2+2x+4y+2=0
x^2+2x+1+4y^2+4y+1=0
(x+1)^2+(2y+1)^2=0
x+1=0 x=-1
2y+1=0 y=-1/2
5x^2+16y^2
=5(-1)^2+16(-1/2)^2
=5+4
=9
√9=3