if a>b and a(b-a) =0, which of the following must be true? a=0; b<0; a-b>0 and why?

Answer 1

To get a product of zero, one of the two must be zero, either a or (b-a)... but we know that a > b, thus a-b *can't* be zero.

a = 0 is true, from the logic above.
b < 0 would also be true (because b is less than a, and a = 0)
(a-b) > 0 is also true because zero minus a negative, would be a positive number.

All three statements are true.

Answer 2

a = 0 is true

Since a != b, then "b - a" will never equal 0
Therefore for the equation to equal 0, a must be 0.
And b must be less than zero since a > b...

So...
a = 0 is true (only way to make equation work)
b < 0 is true (because b < a)
a - b > 0 is true (because b < a)

Answer 3

a(b-a)=0 so a=0 or a=b but a>b so a=0, a>b so 0>b.
a>b so a-b>0
so a=0 and b<0 and a-b>0.
all of them is true!