Question

Find four consecutive natural numbers if you know that the product of the first two is 38 less than the product of the following two numbers.

Answer 1

`8,9,10,11`

Explanation:

Let

x------> first natural number

x+1 ---> second consecutive natural number

x+2 ---> third consecutive natural number

x+3 ---> fourth consecutive natural number

we know that

`x(x+1)=(x+2)(x+3)-38`

`x^(2)+x=x^(2)+3x+2x+6-38`

`x^(2)+x=x^(2)+5x+6-38`

`5x-x+6-38=0`

`4x=32`

`x=8`

therefore

The numbers are

`8,9,10,11`

Answer 2

Because the four numbers are consecutive, we can call the first one x, and the other three are x+1, x+2, and x+3, respectively. x * (x+1) = (x+2) * (x+3) - 38 x^2 + x = x^2 + 5x +6-38 x^2 + x = x^2 + 5x - 32 -4x = -32 x=8 The four numbers are 8, 9, 10, and 11 check solution: 8*9=10*11-38 72=110-38 72=72