Question

Find a natural number whose square diminished by 84 is equal, to thrice of 8 more than the given number.

Answer 1

Step 1: Construct the equation based on given condition.
let n be the required natural number.
According to question,
$n^2-84=3(n+8)$
$\Rightarrow n^2-3n-108=0$

Step 2: Find the roots using factorization.
By splitting the middle term, we get :
$n^2-(12n-9n)-108=0$
$\Rightarrow n^2-12n+9n-108=0$
$\Rightarrow n(n-12)+9(n-12)=0$
$\Rightarrow (n-12)(n+9)=0$
$\Rightarrow n=12$ and $n=-9$.
Since, natural numbers cannot be negative.
hence, the required natural number is $12$.