Let us assume age of zia = x years.
Raj is three years older than Zia.
Therefore, Raj age = (x+3).
Sum of squares of their ages = 369.
Therefore, we can set an equation as :
[tex]x^2 +(x+3)^2 = 369[/tex]
Let us expand [tex](x+3)^2[/tex] now.
[tex](x+3)^2 = x^2+ 6x+9[/tex]
[tex]x^2+x^2+ 6x+9 = 369.[/tex]
Subtracting 369 from both sides
[tex]2x^2+ 6x+9 -369 = 369 -369.[/tex]
[tex]2x^2+ 6x -360 =0[/tex]
Factoring quadratic
[tex]2\left(x-12\right)\left(x+15\right)=0[/tex]
[tex]x=12,\:x=-15[/tex]
We can't take negative value for age.
Therefore, Zia's age is 12 years and Raj age is 12+3 = 15 years.
