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

Question

Philoid · Accepted Answer

Let the natural number be x,

Square of a number and diminished by 84

= (x² + 84)

Thrice of 8 more than the given number

= 3(x + 8)

Equating both the equations,

⇒ x² – 84 = 3(x + 8)

⇒ x² – 84 = 3x + 24

∴ x² - 3x – 108 = 0

Using the quadratic formula,

∴ The natural number . (* A natural number cannot be negative)