Find two consecutive natural numbers whose product is 20.
Answers
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..
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.