若x,y为实数,且满足x²+(根号x-6)-6xy+9y²=0,则4x+3y²的算术平方根是?

问题描述:

若x,y为实数,且满足x²+(根号x-6)-6xy+9y²=0,则4x+3y²的算术平方根是?

x²+(根号x-6)-6xy+9y²=0
x²-6xy+9y²+(根号x-6)=0
(x-3y)^2+(根号x-6)=0
(根号x-6)=0
x=6
x-3y=0
6-3y=0
y=2
√(4x+3y^2)
=√(4*6+3*2^2)
=√36
=±6