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assume() seems not to work for a specific case...

Hi, experts

I tried the following commands:

var('a, b, c')
assume(a>0, b>0, c>0)
solve([a*(b+c)==0, b*(c-a)==0, c*(a+b)==0], a,b,c)

expecting sage to return only (a,b,c) = (k, -k, k).

However, sage returned
(a,b,c) = (k, 0, 0), (0, k, 0), (0, 0, k), (k, -k, k).
though I typed 'assume(a>0, b>0, c>0)'.

Is there any way to invalidate the first 3 answers ?