Problem
\( \begin{array}{l}a+b+c=4 \\ a^{2}+b^{2}+c^{2}=10 \\ a^{3}+b^{3}+c^{3}=22 \\ a^{4}+b^{4}+c^{4}=?\end{array} \)
Solution
Step 1 ：\(a^3 + b^3 + c^3 - 3abc = (a + b + c)((a + b + c)^2 - 3(ab + bc + ca))\)
Step 2 ：\((a^2 + b^2 + c^2)^2 = (a^3 + b^3 + c^3 - 3abc)^2\)
Step 3 ：\(a^4 + b^4 + c^4 = (a^4 + b^4 + c^4 - 4a^3b^3 + 2a^2b^2c^2) = 2(a^2 + b^2 + c^2)^2 - (a^3 + b^3 + c^3)^2\)
