Question

If `x+y=19` and `xy=78`, find `y-x`?

Answer 1

`y-x=+-7`

Explanation:

As `x+y=19` and `xy=78`, we have

`(x+y)^2=x^2+2xy+y^2`

i.e. `19^2=x^2+y^2+2xx78`

i.e. `x^2+y^2=19^2-2xx78=361-156=205`

Hence, `(y-x)^2=y^2+x^2-2xy=205-2xx78=205-156=49`

and `y-x=+-7`

In fact we can solve for `x` and `y` and the two numbers will be `13` and `6` or `6` and`13`.