# The Vitals of Mathematics

Algebra Level 5

$a+b+c=\lambda$ for positive real variables $a,b,c$ .
Let $S_1=\sum \limits_{cyc} \frac{a^2}{\lambda-a}$ and $S_2=\sum \limits_{cyc} \frac{1}{\lambda-a}$.
We define a function $f(t)$ such that $f(S_2)=S_1$. If $f'(t) = 9$ for all values of $t$ in the domain, determine the value of $\lambda$.

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