Question

If a>b and a(b-a)=0, which one or more of the following must be true?

i) a=0 ii) b<0 iii) a-b>0

Answer 1

`a\ \textgreater \ b \Rightarrow a-b\ \textgreater \ 0 \\ \\a(a-b)=0 \Rightarrow a=0 \\ \\a\ \textgreater \ b \\0\ \textgreater \ b \\b\ \textless \ 0`

All options are correct.