James is solving a number puzzle that involves three integers, a, b, and c, where c is a positive integer. The product of a and b is 6. The product of a and c is -4. The product of b and c is -6.

Given:

Three integers, a, b, and c, where c is a positive integer.

The product of a and b is 6.

The product of a and c is -4.

The product of b and c is -6.

To find:

The values of a,b and c.

Solution:

According to the given information:

       ...(i)

      ...(ii)

     ...(iii)

From (ii), we get

         ...(iv)

From (iii), we get

        ...(v)

Putting  and in (i), we get

Taking square root on both sides, we get

It is given that c is a positive integer. So, it cannot be negative and the only value of c is .

Putting in (iv), we get

Putting in (v), we get

Therefore, the values of a,b,c are .

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