Question

Four brothers have ages which are consecutive even integers. If the product of the ages of the two middle brothers is 528, how old is the oldest brother?

**must use algebra**

Answer 1

The oldest brother is of age
`26` years.

Explanation:

As the age of four brothers are consecutive even integers.

We assume that the ages are
`x,(x+2),(x+4),(x+6)` as their respective ages.

And the age of the youngest brother
`x` yrs.

Age of the oldest brother
`(x+6)` yrs.

According to the question

Product of two middle brother that is
`(x+2)(x+4) =528`

So we will arrange this in our equation and solve the quadratic.

`(x+2)(x+4) =528`

`x^(2)+4(x)+2(x)+8 =528`

`x^(2)+4(x)+2(x)+8-528=0`

`x^(2)+6(x)-520=0`

Solving the quadratic by using middle term splitting or directly with quadratic formula we can find the value of 'x' .

Here it is solved with quadratic formula:

Comparing with standard equation
`ax^(2)+b(x)+c=0`,here
`a=1,b=6\ and\ c=-520`.

`x= (-b \pm √(b^2-4ac) )/(2a) = (-6 \pm √(6^2-4* \ (-520)) )/(2* 1)`

`x=20,-26`

We will work with the positive value of (x) so the the age of the youngest brother
`=(x)=20` yrs.

And the age of the the oldest brother
`=(x+6)=(20+6)=26` years.

The age difference is of
`(26-20)=6` years.