# Find two consecutive natural numbers whose product is 20.

Question:

Find two consecutive natural numbers whose product is 20.

Solution:

Let two consecutive numbers be $x$ and $(x+1)$

Then according to question

$x(x+1)=20$

$x^{2}+x-20=0$

$x^{2}+5 x-4 x-20=0$

$x(x+5)-4(x+5)=0$

$(x+5)(x-4)=0$

$(x+5)=0$

$x=-5$

Or

$(x-4)=0$

$x=4$

Since, being a natural number,

Therefore negative value is not possible

So when $x=4$ then

$x+1=4+1$

$=5$

Thus, two consecutive numbers are 4,5