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A(a-2)x=4(a-2) When A meets what conditions, X has only one solution, no solution and countless solutions? (Senior one math problem)
No solution a=0

Countless solutions a=2

The unique solution A is not equal to 2, and A is not equal to 0.

Solution process

When a(a-2)=0 and 4(a-2) is not equal to 0, there is no solution, so find a=0.

When a(a-2)=0 and 4(a-2)=0, there are countless solutions, so a=2 is found.

When a(a-2) is not 0 and 4(a-2) is not 0, the unique solution A is not equal to 2 and A is not equal to 0.