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find Integer value of a for which the equation |2x+1|+|x-2|=a have only integer roots.
If I am interpreting this correctly, I would start with partitioning the real line by the zeros of the function stuck into the absolute values: -1/2 and 2
x <= -1/2
You get: -(2x+1)-(x-2)=a
-1/2 < x <= 2
You get: (2x+1)-(x-2)=a
x > 2
You get: (2x+1)+(x-2)=a
In the first case: -3x+1=a gives the only possible integer values a=1-3k for which x=k will be a root.
Try the others.
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