Question

关于x的方程3x2-(4m2-1)x+m(m+2)=0的两实数根之和等于两实数根的倒数和,求m的值

Answer 1

x1+x2=(4m^2-1)/3

x1x2=m(m+2)/3

又：x1+x2=1/x1+1/x2=(x1+x2)/(x1x2)

得：x1+x2=0 or x1x2=1

1),x1+x2=0,4m^2-1=0 m=1/2,or -1/2

2)x1x2=1,m(m+2)=3,m^2+2m-3=0,(m+3)(m-1)=0,m=1 or -3