Question

find a natural no. whose square diminshed by 84 is equal to thrice of eight more than the given no

Answer 1

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.

Answer 2

Hi,

Here is your answer,

Let the number be a

AQT,

a² - 84 = 3(a+8)

→ a² - 84 = 3a +24

→ a² - 3a - 108 = 0

→ a²- 12a + 9a - 108 = 0

→ a(a-12) +9(a-12) = 0

→ (a-12)(a+9) = 0

a = 12 and - 9

But it is a natural number, 

So, a = 12

Required number = 12



Hope it helps you !