Let's assume
Raj's age is x years
Zia's age is y years
we are given
Raj is three years older than zia
so, we get
[tex]x=y+3[/tex]
now, we can solve for y
[tex]y=x-3[/tex]
the sum of the squares of their ages is 369
so, we get
[tex]x^2+y^2=369[/tex]
now, we can plug back y
[tex]x^2+(x-3)^2=369[/tex]
now, we can solve for x
[tex]2x^2-6x+9=369[/tex]
[tex]2x^2-6x-360=0[/tex]
[tex]x^2-3x-180=0[/tex]
[tex](x+12)(x-15)=0[/tex]
[tex]x=-12 , x=15[/tex]
Since, age can not be negative
so, we will only consider positive
[tex]x=15[/tex]
now, we can find y-value
[tex]y=15-3[/tex]
[tex]y=12[/tex]
So,
Raj's age is 15 years
Zia's age is 12 years...........Answer
