Question

if the sum of 2 numbers is 31 and their product is 240 then find the absolute difference between the numbers

Answer 1

Hey !!!!!!

let the numbers be x and y

Then ATQ,

x + y = 31

=> y = 31 - x

Also x * y = 240

Substituting the value of y

=> x( 31 - x) = 240
=> 31x - x² = 240
=> x² - 31x + 240 = 0

We'll solve this by completing the square.

=> x² - 31x + (31/2)² = -240 + (31/2)²
=> x² - 31x +(31/2)² = -240 + 961/4
=> x² - 31x + (31/2)² = (961 - 960)/4
=> (x - 31/2)² = 1/4
=> x - 31/2 = +- √1/4
=> x - 31/1 = +-1/2
=> x = (31 + 1)/2. or => x = (31-1)/2

Thus x = 16 or 15

Thus y = 31 - 15
=> y = 16

Thus the numbers are 16 and 15

Their difference = 16 - 15
=> 1

Hope this helps

Answer 2

Answer:

1

Step-by-step explanation:

Let the numbers be x and (31-x)

x(31-x) = 240

x^2–31x+240 = 0

(x-15)(x-16) = 0