Question

1.如果a.b .c .为非零的有理数,有理数K=a/(b+C) =b/(a+c )=c/(a+b) .请求出K的值.

Answer 1

K=a/(b+C) =b/(a+c )=c/(a+b)

a=kb+kc

b=ka+kc=k^2b+k^2c+kc,b=(k^2c+kc)/(1-k^2)

c=ka+kb=k^2b+k^2c+kb=k^2c+(k^2+k)*(k^2c+kc)/(1-k^2)

1-k^2=k^2(1-k^2)+(k^2+k)^2

1-k^2=k^2-k^4+k^4+2k^3+k^2

2k^3+3k^2-1=0

(k+1)^2(2k-1)=0

k1=-1,k2=1/2