Question

the difference between the squares of two consecutive numbers is 31 .find the numbers ​

Answer 1

Step-by-step explanation:Two consecutive no.s are x and x + 1

squares of both the no.s is x^2 and (x + 1)^2

their difference is 31

The equation forms like this :

x^2 - [(x + 1)^2] = 31

x^2 - [ x^2 + 1^2 + 2 * x * 1] = 31

x^2 - [ x^2 + 1 + 2x] = 31

x^2 - x^2 - 1 - 2x = 31

- 1 - 2x = 31

- 2x = 31 + 1

- 2x = 32

x = 32/-2

x = - 16

x + 1 = -16 + 1 

        = - 15

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Answer 2

Answer:

The formula for the differences between consecutive perfect squares is:

2n + 1 where n represents the lower of the consecutive numbers being squared.

2n + 1 = 31 : subtract 1 from both sides

2n = 30 : divide both sides by 2

n = 15 and the next number is 16.

Check: 16² - 15² = 256 - 225 = 31 Solution checks

15 and 16