SOLUTION: Find two negative numbers such that the square of their sum is 20 more than the square of their difference, and the difference of their squares is 24. I have an upcoming mathlet

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Question 10603: Find two negative numbers such that the square of their sum is 20 more than the square of their difference, and the difference of their squares is 24.
I have an upcoming mathletes compitition, and this problem has me stumpted.
Answer by longjonsilver(2297) (Show Source):
You can put this solution on YOUR website!
let 2 numbers be x and y.

--eqn1
also, --eqn2

eqn1 becomes

... now square both sides
so,
which is

eqn2 becomes

Sub this into eqn1, to give

..just take the negative version, since the question asked for that.

now, , so
--> x^2 = 289/11
-->
-->

check:
is 44
is 13.09
so this is wrong!, since it should differ by 20.

and is 289/11 - 25/11 which is 24... correct.

so there might be something i am glaringly missing here...check my working: the method is correct!

jon.