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?

Question

asked May 1, 2019 159k views

1 Answer

Stewart · Answer 1 · 2019-05-07T02:28:09+0000

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 :

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

Let us expand
(x+3)^2 now.

(x+3)^2 = x^2+ 6x+9

x^2+x^2+ 6x+9 = 369.

Subtracting 369 from both sides

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

2x^2+ 6x -360 =0

Factoring quadratic

$2\left(x-12\right)\left(x+15\right)=0$

$x=12,\:x=-15$

We can't take negative value for age.