Quelqu’un pourrait t’il m’aider s’il vous plaît ? Mary tells him his conjecture couldn't be right for any consecutive numbers. How can Dawson PROBLEME 2 Prove w

Réponse :

Explications étape par étape

Kevin notes that:  

5² - 4² = 9 and 5 +4 = 9

10² -9² = 19 and 10 + 9 = 19

250² - 249² = 499 and 250 + 249 = 499

and therefore, he asserts that the difference between the squares of two consecutive numbers is equal to the sum of these two  numbers.

Let's prove he's right?

Let x and x-1 be the two consecutive numbers

Difference of squares: x² - (x-1) ² = x² - (x² -2x + 1) = x² -x² + 2x -1

                                                      = 2x -1

                                                      = x + x -1

sum of these two  numbers:       x + (x-1)

and so Kevin is right:

The difference between the squares of two consecutive numbers is equal to the sum of these two  numbers.