Question

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

Answer 1

Let the natural number = ‘x’.

According to the question,

We get the equation,

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

Since, natural numbers cannot be negative.

The number is 12.