Question

已知一元二次方程2x�0�5-mx-2m+1=0的两根平方和是4分之29，求m的值

Answer 1

两根之积=（-2m+1)/2两根之和=m/2两根和的平方=两根平方和+2倍的两根之积即m^2/4=29/4+(-2m+1)得m^2+8m-33=0得m=-11或3

Answer 2

x1+x2=m/2x1*x2=(1-2m)/2 x1方+x2方=29/4（x1+x2)方-2x1x2=29/4m方/4-(1-2m)=29/4m方+8m-33=0(m-3)(m+11)=0m=3或m=-11 判别式=m方-8（1-2m)≥0m方+16m-8≥0当m=-11时不满足要求 所以m=3