Question

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

Answer 1

Hi ,

Let the natural number = x

Square of the number = x²

According to the problem given,

x² - 84 = 3 ( x + 8 )

x² - 84 = 3x + 24

x ² - 3x -84 - 24 = 0

x² - 3x - 108 = 0

Splitting the middle term

x² - 12x + 9x - 108 = 0

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

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

Therefore ,

x - 12 = 0 or x + 9 = 0

x = 12 or x = -9

But x is a natural number ,

Therefore ,

Required natural number = x = 12

I hope this helps you.

:)