Question

The sum of the squares of two numbers is 13 and their product is 6. Find :

(i) the sum of the two numbers.

(ii) the difference between them.

Answer 1

Let x and y be the two numbers, then

$x^2+y^2=13andxy=6$

(i) $(x+y{)}^2=x^2+y^2+2xy=13+2\times 6=13+12=25\therefore x+y=\pm \sqrt{25}=\pm 5$

(ii) $(x-y{)}^2=x^2+y^2-2xy=13-12=1\therefore x-y=\pm 1$