m n是正数 0<x<1 证明m^2/(1-x)+n^2/x大于等于（m+n）^2
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[m^2/(1-x)+ n^2/x] - (m+n)^2
=m^2/(1-x)+ n^2/x - m^2 -n^2 -2mn
=m^2[1/(1-x) -1] +n^2[1/x -1] -2mn
=m^2 [x/(1-x)]+n^2[(1-x)/x]-2mn
=[m^2 x^2 +n^2(1-x)^2 -2mnx(1-x)]/[x(1-x)] 0<x<1 =>0<1-x<1
=[mx-n(1-x)]^2 /[x(1-x)] >= 0
=> [m^2/(1-x)+ n^2/x] >= (m+n)^2
=m^2/(1-x)+ n^2/x - m^2 -n^2 -2mn
=m^2[1/(1-x) -1] +n^2[1/x -1] -2mn
=m^2 [x/(1-x)]+n^2[(1-x)/x]-2mn
=[m^2 x^2 +n^2(1-x)^2 -2mnx(1-x)]/[x(1-x)] 0<x<1 =>0<1-x<1
=[mx-n(1-x)]^2 /[x(1-x)] >= 0
=> [m^2/(1-x)+ n^2/x] >= (m+n)^2
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