Question

QUESTION :

PRODUCT OF 4 NATURAL NUMBERS IS " 840 ".

FIND THE NUMBERS :

I NEED IT .....

DO IT FAST ......

^_^ ^_^ ^_^ ^_^ ^_^ ^_^

❤❤❤❤❤❤❤❤❤❤❤



​

Answer 1

The natural numbers can be written as :-

a , a + 1 , a + 2 , a + 3 .

Product of 4 natural numbers is given 840 .

⇒ a ( a + 1 )( a + 2 )( a + 3 ) = 840

⇒ a ( a + 3 )( a + 1 )( a + 2 ) = 840

⇒ ( a² + 3 a )( a² + a + 2 a + 2 ) = 840

⇒ ( a² + 3 a )( a² + 3 a + 2 ) = 840

⇒ ( a² + 3 a + 1 - 1 )( a² + 3 a + 1 + 1 ) = 840

Using ( a + b )( a - b ) = a² - b² :-

⇒ ( a² + 3 a + 1 )² - 1 = 840

⇒ ( a² + 3 a + 1 )² = 841

⇒ a² + 3 a + 1 = ± 29

Neglect the negative sign :-

⇒ a² + 3 a - 28 = 0

⇒ a² + 7 a - 4 a - 28 = 0

⇒ a ( a + 7 ) - 4 ( a + 7 ) = 0

a = 4 neglecting the negative value .

So numbers are a , a + 1 , a + 2 , a + 3

⇒ 4 , 5 , 6 , 7

The numbers are 4 , 5 , 6 , 7 .