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The product of four consecutive natural numbers is 5040.find the numbers​

Answer»

Answer:

x = 7, x + 1 = 7 + 1 = 8, x + 2 = 7 + 2 = 9, x + 3 = 7 + 3 = 10

X = 7, 8, 9, 10

Step-by-step explanation:

GIVEN The product of FOUR consecutive NATURAL number is 5040.Find those numbers

Let the four consecutive natural numbers be x, (x+1), (x+2) and (x+3)

 So we can write as x (x + 3) (x + 1)(x + 2) = 5040

 We get (x^2 + 3 x)(x^2 + 3 x + 2) = 5040

 Add and subtract 1 for the first term, so

             ((x^2 + 3 x + 1) - 1 } {(x^2 + 3 x + 1) + 1} = 5040

       (x^2 + 3 x + 1)^2 - 1^2 = 5040

         (x^2 + 3 x + 1 )^2 = 5041

      x^2 + 3 x + 1 = 71

      x^2 + 3 x - 70 = 0

     x^2 + 10 x - 7 x - 70 = 0

     x (x + 10) - 7(x + 10) = 0

     (x + 10) (x - 7) = 0

    x = - 10 , 7

 So taking x = 7, since it is a natural number we get

  x = 7, x + 1 = 7 + 1 = 8, x + 2 = 7 + 2 = 9, x + 3 = 7 + 3 = 10

The numbers are 7, 8, 9, 10


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