Question

Find the two numbers whose sum is 43 and the product is 462.

Answer 1

Answer:

21 and 22

Step-by-step explanation:

Let the two numbers be x and y

According to given

x + y = 43 - - - (1)

xy = 462 - - - (2)

=> y = 462/x

Putting the value of y in (1)

=> x² - 43x + 462 = 0

=> x² - 21x - 22x + 462 = 0

=> x(x - 21) - 22(x - 21) = 0

=> (x - 21)(x - 22) = 0

=> x = 21 or 22

So y is either 22 or 21

So required numbers are 21 and 22

Answer 2

In context to questions asked,

We have to determine the value of the number.

As per questions,

Sum of both the number= 43

Product of both the number = 462

So, let the number be x and y

So,

$x + y = 43 = > x = 43 - y \\ xy = 462$

So, putting the value of X in term of y in second equation,

So, we will get,

$(43 - y) \times y = 462 \\ 43y - {y}^{2} = 462 \\ 43y - {y}^{2} - 462 = 0 \\ {y}^{2} - 43y + 462 = 0 \\ {y}^{2} - 21y - 22y+ 462 = 0 \\ y = 21 \: and \: 22$

Hence, value of both the number will be 21 and 22.