已知m+n=-1,mn=-1/2,求[(n+10/(m+10]+[(m+1)/(n+1)的值
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已知m+n=-1,mn=-1/2,求[(n+10/(m+10]+[(m+1)/(n+1)的值
答案好像是-4,但是不知怎么化简
答案好像是-4,但是不知怎么化简
![已知m+n=-1,mn=-1/2,求[(n+10/(m+10]+[(m+1)/(n+1)的值](/uploads/image/z/17303516-44-6.jpg?t=%E5%B7%B2%E7%9F%A5m%2Bn%3D-1%2Cmn%3D-1%2F2%2C%E6%B1%82%5B%28n%2B10%2F%28m%2B10%5D%2B%5B%28m%2B1%29%2F%28n%2B1%29%E7%9A%84%E5%80%BC)
是不是(n+1)/(m+1)+(m+1)/(n+1)?
(n+1)/(m+1)+(m+1)/(n+1)
=[(n+1)^2+(m+1)^2]/(m+1)(n+1)
=(m^2+n^2+2m+2n+2)/(mn+m+n+1)
=[(m+n)^2-2mn+2(m+n)+2]/[(mn+(m+n)+1]
=[(-1)^2-2*(-1/2)+2*(-1)+2]/[-1/2+(-1)+1]
=(2)/(-1/2)
=-4
(n+1)/(m+1)+(m+1)/(n+1)
=[(n+1)^2+(m+1)^2]/(m+1)(n+1)
=(m^2+n^2+2m+2n+2)/(mn+m+n+1)
=[(m+n)^2-2mn+2(m+n)+2]/[(mn+(m+n)+1]
=[(-1)^2-2*(-1/2)+2*(-1)+2]/[-1/2+(-1)+1]
=(2)/(-1/2)
=-4
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