Ah! A use for perl's flip-flip operator:

#!/usr/bin/perl -w

while (<DATA>) {
    next if m|</root>|..m|<root>|;
    print;
}
print "</root>\n";

__DATA__
<?xml version="1.0" encoding="UTF-8"?>
<root>
  <some_xml></some_xml>
</root>
<?xml version="1.0" encoding="UTF-8"?>
<root>
  <some_xml></some_xml>
</root>
<?xml version="1.0" encoding="UTF-8"?>
<root>
  <some_xml></some_xml>
</root>
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