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Sergio [31]
2 years ago
13

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.
Mathematics
1 answer:
m_a_m_a [10]2 years ago
8 0

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:

ab=6        ...(i)

ac=-4       ...(ii)

bc=-6      ...(iii)

From (ii), we get

a=-\dfrsc{4}{c}          ...(iv)

From (iii), we get

b=-\dfrsc{6}{c}         ...(v)

Putting a=-\dfrsc{4}{c}  and b=-\dfrsc{6}{c} in (i), we get

\dfrac{-4}{c}\times \dfrac{-6}{c}=6

\dfrac{24}{c^2}=6

\dfrac{24}{6}=c^2

4=c^2

Taking square root on both sides, we get

\pm \sqrt{4}=c

\pm 2=c

It is given that c is a positive integer. So, it cannot be negative and the only value of c is c=2.

Putting c=2 in (iv), we get

a=-\dfrsc{4}{2}

a=-2

Putting c=2 in (v), we get

b=-\dfrsc{6}{2}

b=-3

Therefore, the values of a,b,c are a=-2,b=-3,c=2.

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