Adam is 2 years older than mike. the square of adam's age is 28 greater than the square of mike's age in years. what is the sum of adam's age and mike's age

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.

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