Question

已知方程x^2+(m+9)x+2m+6=0的两根平方和为24,

Answer 1

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!