Question

Find a natural no whose square diminished by 84is equal to thrice of 8more than the given no

Answer 1

Let the natural no. be x
Acc . to the given conditions:
${x}^{2} - 84 = 3(x + 8) \\ {x}^{2} - 84 = 3x + 24 \\ {x}^{2} - 3x - 108 = 0 \\ {x}^{2} + 9x - 12x - 108 = 0 \\ x(x + 9) - 12(x + 9) = 0 \\ (x - 12)(x + 9) \\ x = 12 \: or \: - 9$

A natural no. can't be negative.
therefore the given no. is 12