Question -
Answer -
Let n be a required natural number.
Square of a natural number diminished by 84 = n2 – 84
and thrice of 8 more than the natural number = 3 (n + 8)
Now, by given condition,
n2 – 84 = 3 (n + 8)
=> n2 – 84 = 3n + 24
=> n2 – 3n – 108 = 0
=> n2 – 12n + 9n – 108 = 0 [by splitting the middle term]
=> n (n – 12) + 9 (n – 12) = 0
=> (n – 12) (n + 9) = 0
=> n = 12 [n ≠ – 9 because n is a natural number]
Hence, the required natural number is 12.