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

Options

A. 10
B. 11
C. 12
D. 13

Answer

C

Explanation

Let `n` be a required natural number.
Square of a natural number diminished by `84=n^(2)-84`
and thrice of 8 more than the natural number `=3(n+8)`
Now, by the given condition,
`n^(2)-84=3(n+8)`
`impliesn^(2)-84=3n+24`
`implies n^(2)-3n-108=0`
`implies n^(2)-12n+9n-108=0` [by splitting the middley term]
`= n(n-2)+9(n-12)=0`
`implies (n-12)(n+9)=0`
`implies n=12` [ `:'!=-9` because `n` is a natural number]
Hence the required natural number is 12.