The difference between the squares of two consecutive numbers is 35. The numbers are?Options19&2018&1716&1817&2017&18

The problem can be solved by using the formula for the difference of squares, which is a^2 - b^2 = (a+b)(a-b).

Given that the difference between the squares of two consecutive numbers is 35, we can set up the equation as follows:

(a+b)(a-b) = 35

Since the numbers are consecutive, we know that a - b = 1. We can substitute this into the equation:

(a + b)(1) = 35

This simplifies to a + b = 35.

We can then solve for a and b by trying out the options given:

Option 1: 19 & 20 19 + 20 = 39, which is not equal to 35.

Option 2: 18 & 17 18 + 17 = 35, which is equal to 35.

Option 3: 16 & 18 16 + 18 = 34, which is not equal to 35.

Option 4: 17 & 20 17 + 20 = 37, which is not equal to 35.

Option 5: 17 & 18 17 + 18 = 35, which is equal to 35.

Therefore, the numbers are 18 & 17 and 17 & 18.