Answer: 20 and 14
Step-by-step explanation:
Using a little guess and check, we can figure out that the numbers are 6 apart and the difference between their squares is 204.
[tex]20^2 = 400\\14^2=196[/tex]
[tex]20^2-14^2 = 204[/tex]
A trick to doing this is to start with a number that is easily squared like 10 or 20 and see if the difference between their numbers is larger or smaller and change your numbers based on them.
Hope this helped :)
Answer:
14 and 20
Step-by-step explanation:
Let x and y be two numbers where x < y.
We are given :
y - x = 6
y² - x² = 204
Then
y - x = 6
(y - x)(y + x) = 204
Then
y - x = 6
6 × (y + x) = 204
then
y - x = 6 (Equation 1)
y + x = 34 (Equation 2)
Then
(Equation 1) + (Equation 2) ⇒ 2y = 40 ⇒ y = 20
Now ,we substitute y by 20 in equation 1 :
y - x = 6
⇔ 20 - x = 6
⇔ 20 - 6 = x
⇔ x = 14
