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.

K=a/(b+C) =b/(a+c )=c/(a+b) a=kb+kcb=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)^21-k^2=k^2-k^4+k^4+2k^3+k^22k^3+3k^2-1=0(k+1)^2(2k-1)=0k1=-1,k2=1/2