First, two previously known lemmas about multiple spring systems that you can assume to be true or derive for yourself:

(1) In parallel, so

(2) In series, so

Start with , ,

because these are in series, so . Since the load is split evenly between springs #1 and #2, we can assume .

(i) Assume so WLOG . So or . Since , . Solving for gives . By lemma 2,

(ii) By lemma 1, and by lemma 2,

In each instance of course,