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## Explanation

- The difference between two integers is 5.
- Their product is 500.
- The number will be figure out in this way.

Let suppose the integers are y and z.

The difference between two integers is 5

y – z = 5 ________ (i)

The product of the integers is 500

yz = 500 ________ (ii)

By solving equation (i) and (ii) simultaneously, we can easily find out the value of y (y = 25) and z (z = 20).

## To Find

Numbers = ?

## Solution

Let suppose

Integers are y and z.

According to the given conditions

y – z = 5 ________ (i)

yz = 500

y = 500/z ________ (ii)

Putting y = 500/z in equation (i)

500/z – z = 5

500 – z^{2} = 5z

z^{2} + 5z – 500 = 0

z^{2} + 25z – 20z – 500 = 0

z(z + 25) – 20(z + 25) = 0

(z + 25)(z – 20) = 0

z + 25 = 0 & z – 20 = 0

z = -25 (not possible) & z = 20 (possible)

Put z = 20 in equation (i)

y – 20 = 5

y = 5 + 20

y = 25

**Required Numbers = 20 & 25 answer**

## Conclusion

The difference between two integers is 5. Their product is 500. The numbers are 20 and 25.