7. Given the function $f(x)=x^{3}-2 x^{2}-3 x+4$, if $f(a)=f(b)=f(c)$, where $a<b<c$, then $a^{2}+b^{2}+c^{2}=$
Given $f(a)=f(b)=f(c)=k \Rightarrow a, b, c$ are the roots of the equation $f(x)-k=x^{3}-2 x^{2}-3 x+4-k=0$, $\left\{\begin{array}{l}a+b+c=2 \\ a b+b c+c a=-3, \Rightarrow a^{2}+b^{2}+c^{2}=(a+b+c)^{2}-2(a b+b c+c a)=10 \\ a b c=k-4\end{array}\right.$