1.1/a+1/b=1/(a+b),则b/a+a/b=2.若方程x/(x-3)-2=m-1/x-3有增根,求m的值

Question

1.1/a+1/b=1/(a+b),则b/a+a/b=
2.若方程x/(x-3) -2=m-1/x-3有增根,求m的值

Answer 1

1/a+1/b=1/(a+b)
b(a+b)+a(a+b)=ab,a^2+b^2=ab
则b/a+a/b=(a^2+b^2)/ab=1.
2.x/(x-3) -2=m-1/x-3
x-2(x-3)=m-1
x=7-m
因为方程有增根 x=3
令 7-m=3,
m=4