Question

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

Answer 1

x^2+4y^2+2x-4y+2=0

x^2+2x+1+4y^2-4y+1=0

(x+1)^+(2y-1)^2=0

x+1=0 x=-1

2y-1=0 y=1/2

5x^2+16y^2

=5+16(1/2)^2

=5+4

=9

√9=3