If $$a,b,c$$ are positive integers such that $$ab$$ and $$a^2-ab-ac+bc = 7$$. then the value of $$a-c$$ is

Question

If $$a,b,c$$ are positive integers such that $$a>b$$ and $$a^2-ab-ac+bc = 7$$. then the value of $$a-c$$ is

Uniteasy Admin · Accepted Answer

$$a^2-ab-ac+bc $$
$$=a(a-b)-c(a-b)$$
$$=(a-b)(a-c)=7$$
Since 7 is a prime number, it has only 1 and itself as its factors.
$$a > b $$ implies $$a-c>0$$
Therefore
the value of $$a-c$$ is $$1 $$ or $$7$$
D is the right choice

Multiple Choice Question (MCQ)

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