Question

raj and his sister zia are both at secondary school. Raj is three years older than zia. the sum of the squares of their ages is 369. How old are they?

Answer 1

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

$x^{2}+(x+3)^{2}=369$

$x^{2}+x^{2}+6x+9=369$

$2x^{2}+6x+9=369$

$2x^{2}+6x-360=0$

Factoring 2 out we have,

$x^{2}+3x-180=0$

Now solving this equation,

$x^{2}+15x-12x-180=0$

$x(x+15)-12(x+15)$

$(x+15)(x-12)$

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