( 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} )

Question

( 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} )

Accepted Answer

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)

Answer

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)

\( \begin{array}{l}a+b+c=4 \\ a^{2}+b^{2}+c^{2}=10 \\ a^{3}+b^{3}+c^{3}=22 \\ a^{4}+b^{4}+c^{4}=?\end{array} \)

Answer

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