The product of two numbers is 24 and their sum is 14. Find the numbers.

Given :

The product of the two numbers is 24 and their sum is 14.

To do :

We have to find the numbers.

Solution :

Let the numbers be a and b.

Therefore,

$a + b = 14$

$b = 14-a$       -----(1)

$a \times b = 24$

$a \times (14-a) = 24$    [from (1)]

$a(14) - a(a) = 24$

$a^2-14a+24 = 0$

$a^2-12a-2a+24 = 0$

$a(a-12)-2(a-12) = 0$

$(a-12)(a-2)=0$

$a=12$ or $a=2$

If $a = 12$,

$b = 14-12 = 2$    [from (1)]

If $a = 2$,

$b = 14-2 = 12$    [from (1)]

The required numbers are 2 and 12.

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Updated on: 10-Oct-2022

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