Busca dos números consecutivos de manera que la diferencia de sus cuadrados sea 19

The numbers are 9 and 10.

Let x be the first number. Since they are consecutive, this means (x+1) represents the second number.

The square of x is x². The square of (x+1) is

(x+1) ² = (x+1) (x+1) = x²+1x+1x+1=x²+2x+1

The difference of these squares would be given by

x²+2x+1 - x²

Setting this equal to 19,

x²+2x+1 - x² = 19

Combining like terms,

2x+1=19

Subtract 1 from each side:

2x+1-1=19-1

2x=18

Divide both sides by 2:

2x/2 = 18/2

x = 9

The first number, x, is 9. This means the second number, x+1, is 9+1=10.