Let Zia's age be = x years
Raj is three years older than Zia, so Raj's age = x+3 years
As the sum of the squares of their ages is 369, so
[tex]x^{2}+(x+3)^{2}=369[/tex]
[tex]x^{2}+x^{2}+6x+9=369[/tex]
[tex]2x^{2}+6x+9=369[/tex]
[tex]2x^{2}+6x-360=0[/tex]
Factoring 2 out we have,
[tex]x^{2}+3x-180=0[/tex]
Now solving this equation,
[tex]x^{2}+15x-12x-180=0[/tex]
[tex]x(x+15)-12(x+15)[/tex]
[tex](x+15)(x-12)[/tex]
x=-15 and x=12
Neglect the negative value as x cannot be negative
So x=12
Hence, Zia's age is 12 years and
Raj's age is 12+3 = 15 years
