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Find two consecutive natural numbers whose product is 20.
Given:
Product of two consecutive natural numbers is 20.
To do:
We have to find the numbers.
Solution:
Let the two consecutive natural numbers be $x$ and $x+1$.
According to the question,
$x(x+1)=20$
$x^2+x=20$
$x^2+x-20=0$
Solving for $x$ by factorization method, we get,
$x^2+x-20=0$
$x^2+5x-4x-20=0$
$x(x+5)-4(x+5)=0$
$(x-4)(x+5)=0$
$x-4=0$ or $x+5=0$
$x=4$ or $x=-5$
$-5$ is not a natural number.
Therefore, the two consecutive natural numbers whose product is 20 are $4$ and $4+1=5$.
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