Question

若x1,x2是关于x的方程x2(2k+1)x+k+1=0的两个实数根,且x1,x2都大于0

Answer 1

是不是X^2+(2k+1)x+k+1=0?

由X1/X2=1/2可得X1=2X2,且x1+X2=-(2K+1),X1X2=K+1,

即3X1=-(2K+1),X1^2=k+1,

再把X1=-(2K+1)/3,X1^2=k+1(即X=-(2K+1)/3,X^2=k+1)代入X^2+(2k+1)x+k+1=0得 (k+1)^2-(2K+1)^2/3+k+1=0最后求得K值.