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:The oldest brother is of age [tex]26[/tex] years.Step-by-step explanation:As the age of four brothers are consecutive even integers.We assume that the ages are [tex]x,(x+2),(x+4),(x+6)[/tex] as their respective ages.And the age of the youngest brother [tex]x[/tex] yrs.Age of the oldest brother [tex](x+6)[/tex] yrs.According to the questionProduct of two middle brother that is [tex](x+2)(x+4) =528[/tex]So we will arrange this in our equation and solve the quadratic.[tex](x+2)(x+4) =528[/tex][tex]x^{2}+4(x)+2(x)+8 =528[/tex][tex]x^{2}+4(x)+2(x)+8-528=0[/tex][tex]x^{2}+6(x)-520=0[/tex]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 [tex]ax^{2}+b(x)+c=0[/tex],here [tex]a=1,b=6\ and\ c=-520[/tex].[tex]x= \frac{-b \pm \sqrt{b^2-4ac} }{2a} = \frac{-6 \pm \sqrt{6^2-4\times \ (-520)} }{2\times 1}[/tex][tex]x=20,-26[/tex]We will work with the positive value of (x) so the the age of the youngest brother [tex]=(x)=20[/tex] yrs.And the age of the the oldest brother [tex]=(x+6)=(20+6)=26[/tex] years.The age difference is of [tex](26-20)=6[/tex] years.