Math, asked by BrainlyHelper, 1 year ago

Find two consecutive natural numbers whose product is 20.

Answers

Answered by nikitasingh79
17

SOLUTION :  

GIVEN : Product of 2 consecutive natural numbers is 20

Let the two consecutive numbers are  x  & (x + 1)  

A.T.Q

⇒ x ( x + 1 ) = 20

⇒ x² + x = 20

⇒ x² + x - 20 = 0

⇒ x² + 5x - 4x - 20 = 0

[By middle term splitting method]

⇒ x ( x + 5 ) - 4 ( x + 5 ) = 0

⇒ ( x + 5 ) ( x - 4 ) = 0      

⇒ ( x + 5 ) = 0  or   ( x - 4 ) = 0  

⇒  x  = - 5    or  x = 4

Since, x is a natural number so x ≠ - 5. [Natural number can't be  negative]

Therefore, x = 4  

First number (x) = 4  

Second number (x +1) = = 4 + 1 = 5

Hence, the required consecutive natural numbers are 4 and 5.

HOPE THIS  ANSWER WILL HELP YOU..

Answered by Anonymous
6

Answer:


4 and 5


Step-by-step explanation:


Two consecutive numbers are in the form a and a + 1

For example 2 , 3


Given product = 20


Product of a and a + 1 can be written as :


a ( a + 1 ) = 20


This is a typical quadratic equation and can be solved by easy factorisation.

a² + a = 20

⇒ a² + a - 20 = 0


Now we have to split +a the middle portion so that we can factorise the given expression.


⇒ a² + 5 a - 4 a - 20 = 0


Here 5 a - 4 a =  a .

⇒ a ( a - 4 ) + 5 ( a - 4 ) = 0

⇒ ( a + 5 )( a - 4 ) = 0


So a + 5 = 0

a - 4 = 0


These are the two possibilities.


When a - 4 = 0

a = 4 .

Numbers are 4 and 4 + 1 = 5


When a + 5 = 0

a = - 5

Numbers are -5 and -5 + 1 = - 4


But the question asked for natural numbers and so we should consider only the positive parts.

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