Question

1.已知关于x的方程x^2=(2m+2)x-(m^2+4m-3)中的m为不小于0的整数,并且它的两实根的符号相反,求m的

Answer 1

1,x1+x2=0

2m+2=0

m=-1

x^2-6=0

x^2=6

x=根号6,-根号6

2,(1),判别式=5m^2-4(m+2)(m-3)

=5m^2-4m^2+4m+24

=m^2+4m+24

=(m+2)^2+20>0

方程有实数根

(2),x1+x2=(√5)m/(m+2)

x1x2=(m-3)/(m+2)

x1^2+x^2=(x1+x2)^2-2x1x2

=(5m^2)/(m+2)^2-2(m-3)(m+2)/(m+2)^2=3

5m^2-2m^2+2m+12=3(m-2)^2

3m^2+2m+12=3m^2-12m+12

14m=0

m=0

3,设(x^2-5)/(x-1)=Y

Y+10/Y=7

Y^2-7Y+10=0

(1),Y=(x^2-5)/(x-1)=2

x^2-5=2x-2

x^2-2x-3=0

x1=3 x2=-1

(2),Y=(x^2-5)/(x-1)=5

x^2-5=5x-5

x(x-5)=0

x1=0 x2=5