Respuesta :

x(x + 1) > x + x + 1 + 109     where x and x+1 are the 2 numbers.

x^2 + x > 2x + 110
x^2  - x - 110 > 0

(x - 11)(x + 10) > 0    The critical values are 11 and -10 but number must be natural

So the value of x is 11

The numbers are 11 and 12
Cricetus

The numbers will be "11 and 12".

Let,

  • The number be "x".
  • The two consecutive numbers be "x, x+1"

According to the question,

→            [tex]x(x + 1) > x + x + 1 + 109[/tex]

→               [tex]x^2+x> 2x+110[/tex]

→      [tex]x^2-x-110> 0[/tex]

→ [tex](x-11)(x+10) > 0[/tex]  

                  [tex]x-11>0[/tex]

                         [tex]x> 11[/tex]

and,

                  [tex]x+10> 0[/tex]

                         [tex]x> -10[/tex]

Here, [tex]x = 11[/tex]

and,

       [tex]x+1 = 11+1[/tex]

                [tex]= 12[/tex]

Thus the response above is right.

Learn more about consecutive number here:

https://brainly.com/question/7135685

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