Q. 24.0( 26 Votes )

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

Answer :

Let the natural number be x,

Square of a number and diminished by 84

= (x^{2} + 84)

Thrice of 8 more than the given number

= 3(x + 8)

Equating both the equations,

⇒ x^{2} – 84 = 3(x + 8)

⇒ x^{2} – 84 = 3x + 24

**∴** x^{2} - 3x – 108 = 0

Using the quadratic formula,

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

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