Question

Three times the square of a natural numbers is 363. Find the number.

Answer 1

Let the required natural number be x. Then, by the given condition,
3x² = 363
$\Rightarrow$ x² = $\frac{363}{3}=121$
$\Rightarrow$ x² – 121 = 0
$\Rightarrow$ (x + 11)(x – 11) = 0
$\Rightarrow$ x + 11 = 0 or x – 11 = 0
$\Rightarrow$ x = –11 or x = 11
Since x is a natural number, it cannot be negative.
Therefore, x = 11.