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## Explanation

- If the difference of two numbers is 3.
- And difference of their squares is 39.
- The larger number can be find out in this way.

Let suppose the numbers are y and z.

The difference between two numbers is 3

y – z = 3 ________ (i)

The difference of their squares is 39

y^{2} – z^{2} = 39 ________ (ii)

By solving equation (i) and (ii) simultaneously, we can easily find out the value of y (y = 8) and z (z = 5) in order to find out the larger number (y = 8).

## To Find

Larger number = ?

## Solution

Let suppose

Numbers are y and z.

According to the given conditions

y – z = 3 ________ (i)

y^{2} – z^{2} = 39

As we know that; a^{2} – b^{2} = (a – b)(a + b)

So;

(y – z)(y + z) = 39 ________ (ii)

Put y – z = 3 in equation (ii)

3(y + z) = 39

y + z = 13 ________ (iii)

Adding equation (i) & (iii)

y + y – z + z = 3 + 13

2y = 16

y = 16/2

y = 8

Putting y = 8 in equation (iii)

8 + z = 13

z = 13 – 8

z = 5

**Larger Number = 8 answer**

## Conclusion

If the difference of two numbers is 3 and the difference of their squares is 39, then the large number is 8.