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'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

$x=y+3$

now, we can solve for y

$y=x-3$

the sum of the squares of their ages is 369

so, we get

$x^2+y^2=369$

now, we can plug back y

$x^2+(x-3)^2=369$

now, we can solve for x

$2x^2-6x+9=369$

$2x^2-6x-360=0$

$x^2-3x-180=0$

$(x+12)(x-15)=0$

$x=-12 , x=15$

Since, age can not be negative

so, we will only consider positive

$x=15$

now, we can find y-value

$y=15-3$

$y=12$

So,

Raj's age is 15 years

Zia's age is 12 years...........Answer