令4a*sqrt(1-a^2)=3a
=> 16a^2-16a^4=9a^2
=> 7a^2=16a^4
=> 7=16a^2
=> a^2=7/16
=> a=sqrt(7)/4 or a=-sqrt(7)/4
所以当a=正负根号7除以4的时候,原题成立.