Question

5 mark question long answer type

dont spam​

Answer 1

Let n be a required natural number.

Square of a natural number diminished by 84=n^2-84

and thrice of 8 more than natural number = 3(n+8)

Now, by given condition,

n^2-84=3(n+8)

n^2-84=3n+24

n^2-3n-108=0

n=12

Hence, the required natural number is 12.

Answer 2

Let the natural number be 'x'.

Therefore, according to the question.

x² - 84 = 3(x+8)

x² - 84 = 3x + 24

x² - 3x - 84 - 24 = 0

x² - 3x - 108 = 0

x² - 12x + 9x - 108 = 0

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

(x + 9) (x - 12)

⇒ x = -9 and x = 12

we have to take the positive value because natural numbers cannot be negative.

Therefore, the number is 12.