Question

Two number whose sum 24and product is 143are

Answer 1

Answer:

13 + 11 = 24 and,

13 × 11 = 143

Answer 2

Answer:

13 and 11

Explanation:

Let the numbers be x and y.

According to the question,

x + y = 24  ⇒ x = 24 - y   ... (i)

xy = 143   ... (ii)

Using x = 24 - y in (ii)

(24 - y) y = 143

24y - y² = 143

y² - 24y + 143 = 0   ... (iii)

Factors of 143 are (1 , 143) and (11 , 13)

-11 - 13 = -24

So, (iii) can be written as

y² - 13y - 11y + 143 = 0

⇒ y (y - 13) - 11 (y - 13) = 0

⇒ (y - 13) ( y - 11) = 0

⇒ y - 13 = 0 or y - 11 = 0

⇒ y = 13 or 11

Using this in (i)

x = 24 - 13 or 24 - 11

x = 11 or 13

so, the two numbers are 11 and 13