the product of four consecutive natural numbers is 5040.find the numbers
Answers
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