Question

The product of four consecutive natural numbers is 840. Find the number

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

let four consecutive natural number are X,X +1 ,X+2,X+3 are respectively

according to quation,

X(X+1)(X+2)(X+3)=840

(X+1)(X+2) X (X+3)=840

(x^2+2x+x+2)(x^2+3x)=840

(x^2+3x+2)(x^2+3x)=840

let x^2+3x=a

(a+2)(a)=840

a^2+2a-840=0

a^2+42a-40a-840=0

a(a+42)-40(a+42)=0

(a+42)(a-40)=0

a=-42 or a=40

but naturals number can not be nagative

a=40

but,

x^2+3x=a

x^2+3x=40

x^2+3x-40=0

x^2+8x-5x-40=0

x (x+8)-5(x+8)=0

(x+8)(x-5)=0

X=-8 or X=5

but naturals number cannot be nagative,

1. X=5
2. X+1=5+1=6
3. X+2=5+2=7
4. X+3=5+3=8
5. the natural numbers are 5,6,7 and 8