Question

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

Answer 1

Find a natural number using the given information:

Let the required natural number be $x$.

It is given that square of $x$ when diminished by $84$ is equal to three times of $8$ more than $x$.

According to the given details, the quadratic equation formed is

$x^2-84=3(x+8)$

On simplifying we get,

$$\begin{gathered} \Rightarrow x^2-84=3(x+8) \\ \Rightarrow x^2-3x–84–24=0 \\ \Rightarrow x^2-3x-108=0 \\ \Rightarrow x^2-12x+9x-108=0 \\ \Rightarrow x(x–12)+9(x–12)=0 \\ \Rightarrow (x+9)(x–12)=0 \end{gathered}$$

So, $x=-9,12$

We know that natural numbers are positive. So $x=-9$ is not possible.

Hence, the required natural number is $12$.