Answer:
The sum of Adam´s and Mike´s age is 14.
Step-by-step explanation:
If Adam is two years older than mike y we called Adam´s age as "x" and Mike´s age as "y", we have: x = y + 2.
If square of Adam´s Age is 28 greater than the square of mike´s age ⇒
x² = y² + 28.
Now we have to consider both equation and replace the first in the second one.
⇒ x² = y² + 28, we replace with x= y + 2. ⇒ (y + 2)² = y² + 28
⇒ y² + 4x + 4 = y² + 28 ⇒ y² + 4x + 4 - y² - 28 = 0 ⇒ 4y - 24 = 0
⇒ 4y = 24 ⇒ y = 24/4 ⇒ y = 6. Mike´s age is 6 years.
With the value of "y" we return to first equation and obtain the value of "x".
⇒ x = y + 2 ⇒ x = 6 + 2 ⇒ x= 8. Adam´s age is 8 years.
Summarizing Adam is 8 years old and Mike 6 years old. So the sum of both ages is 14 years.
