Question

Find tow numbers whose sum is 24 and product is 143 ​

Answer 1

Given:

The sum of the two numbers is 24 and the product is 143.

To find:

The two numbers.

Solution:

The two numbers are 11 and 13.

To answer this question, we will follow the following steps:

Let the two numbers be a and b.

Now,

According to the question, we have

$a + b = 24 \: \:$

This can be written as

$a = 24 - b \: \: (i)$

Also,

$ab = 143 \: \: (ii)$

On putting the value of a from (i) in (ii), we get

$(24 - b)b = 143$

${b}^{2} - 24b + 143 = 0$

On solving the above equation,

we get

${b}^{2} - 11b - 13b + 143 = 0$

$b(b - 11) - 13(b - 11) = 0$

$(b - 13)(b - 11) = 0$

$b = 13 \: and \:11$

On putting the value of b = 11 in (i), we get

$a = 24 - 11 = 13$

Similarly,

when b = 13, a = 11

Hence, the two numbers are 11 and 13.

Answer 2

Answer:

11 and 13

Step-by-step explanation:

A+B=24

A=24-B______1

AB=143______2

PUT VALUE OF 1 IN 2

(24-B)B=143

24B-B²=143

B²-24B+143=0

B²-11B -13B +143 =0

B(B-11) -13(B-11]=0

(B-13) (B-11)

B=13 ❤️‍, B=11