OPEN CHALLENGE=THE PRODUCT OF FOUR CONSECUTIVE NATURAL NUMBERS IS 840. FIND THE NUMBERS.
Answers
You can also get this 840 as product by -7,-6,-5,-4
but in question there is said that numbers should be natural therefore we can't take the negative values only use positive number as your answer.
Answer:
4,5,6 and 7
Step-by-step explanation:
What are consecutive natural numbers ?
Consecutive natural numbers are the numbers which are obtained by adding 1 to the previous number and they start from 1.
1 , 2 , 3 .................
Now consecutive natural numbers are of the form :
a , a + 1 , a + 2 , a + 3 for any natural number a .
It is given here that the product of 4 such natural numbers .
We assume the numbers to be :
x , x + 1 , x + 2 , x + 3 where x is a natural number .
Product = 840 .
So x ( x + 1 )( x + 2 )( x + 3 ) = 840
⇒ x ( x + 2 )( x + 1 )( x + 3 ) = 840
⇒ ( x² + 2 x )( x² + 3 x + x + 3 ) = 840
⇒ ( x² + 2 x )( x² + 4 x + 3 ) = 840
⇒ ( x² ( x² + 4 x + 3 ) + 2 x ( x² + 4 x + 3 ) ) = 840
⇒ x⁴ + 4 x³ + 3 x² + 2 x³ + 8 x² + 6 x = 840
⇒ x⁴ + 6 x³ + 11 x² + 6 x = 840
⇒ x⁴ + 6 x³ + 11 x² + 6 x - 840 = 0
Trial and error method .
Putting x = 4 gives us :
⇒ 4⁴ + 6 ( 4 )³ + 11 ( 4 )² + 6 ( 4 ) - 840 = 0
⇒ 256 + 6 ( 64 ) + 11 ( 16 ) + 24 - 840 = 0
⇒ 256 + 384 + 24 + 176 - 840 = 0
⇒ 840 - 840 = 0
Hence x satisfies the value when x = 4 .
Thus the numbers can be x , x + 1 , x + 2 , x + 3
= > 4 , 4 + 1 , 4 + 2 , 4 + 3
= > 4 , 5 , 6 , 7
These are the numbers .