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

Given:

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

 To do:

We have to find the number.

Solution:

Let the required natural number be $x$.

According to the question,

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

$x^2-84=3x+24$

$x^2-3x-84-24=0$

$x^2-3x-108=0$

Solving for $x$ by factorization method, we get,

$x^2-12x+9x-108=0$

$x(x-12)+9(x-12)=0$

$(x+9)(x-12)=0$

$x+9=0$ or $x-12=0$

$x=-9$ or $x=12$

$-9$ is not a natural number. Therefore, the value of $x$ is $12$.

The required natural number is $12$. 

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Updated on: 10-Oct-2022

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