Question: If the sum of two numbers is 10 and their product is 24, find the numbers.

Solution:

According to the question,

Condition I,
The sum of two numbers is 10. Let one of the two numbers be x. Then, the other number is (10-x).

Condition II,
The product of the two numbers is 24.
$or, x × (10-x) = 24$
$or, 10x - x^2 = 24$
$or, x^2 -10x +24 = 0$
$or, x^2 - (6+4)x + 24 = 0$
$or, x^2 -6x -4x +24 = 0$
$or, x(x -6) -4(x -6) = 0$
$or, (x -4)(x -6) = 0$

Either,
$x -4 = 0$
$\therefore x = 4$

Or,
$x -6 = 0$
$\therefore x = 6$

So, when x = 4, the other number is (10-4) = 6.

And, when x = 6, the other number is (10-6) = 4.

Therefore, the required two numbers are 4 and 6.

#SciPiPupil