Question: Find a number which is when added to its square the sum will be 72.


Solution:

Let the required number be x.

According to the question,

When x is added to its square (x²), the sum will be 72.

$or, x^2 + x = 72$
$or, x^2 + x -72 = 0$
$or, x^2 +(9-8)x -72 = 0$
$or, x^2 +9x -8x -72 = 0$
$or, x(x +9) -8(x +9) = 0$
$or, (x -8)(x +9) = 0$

Either,
$x -8 = 0$
$\therefore x = 8$

Or,
$x +9 = 0$
$\therefore x = -9$

Since we need a positive number because it is added to the square of the same number, the required number is 8.

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