x^2+(m+9)x+2m+6=0
设两个根为X1和X2
根据伟达定理
X1+x2=-(M+9)
X1*X2=2M+6
X1^2+X2^2+2X1X2=24+2X1X2
(X1+X2)^2=24+2X1X2
(m+9)^2=24+12+4m
m^2+14m+45=0
(m+9)(m+5)=0
解得m=-9或m=-4.
验证均为实根!