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## Explanation

- If the sum of the two number is 42

- and their product is 437.

The absolute difference between the numbers can be figure out as follows.

Let suppose the numbers are “y” and “z”.

As the sum of two numbers is 42.

y + z = 42 __________ (i)

The product is 437 so,

yz = 437 __________ (ii)

Through equation (i) and (ii), we can find out the difference between the numbers (y – z).

## To Find

Difference between the numbers = ?

## Solution

Let suppose

Numbers = y and z

Now; according to given condition

y + z = 42 ________ (1)

yz = 437 ________ (2)

y = 437/z

putting in equation (i)

437/z + z = 42

437 + z^{2} = 42z

z^{2} – 42z + 437 = 0

z^{2} – 23z – 19z + 437 = 0

z (z – 23) – 19 (z – 23) = 0

(z – 19) (z – 23) = 0

z = 19 or z = 23

putting both the values in equation (i) separately

y + 19 = 42

y = 42 – 19

y = 23

or

y + 23 = 42

y = 42 – 23

y = 19

So, numbers are 19 and 23.

**Difference = y – z = 23 – 19 = 4 answer**

## Conclusion

If the sum of the two number is 42 and their product is 437, then the absolute difference between the numbers would be 4.