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Solve the simultaneous equations for \(x,y,z\)


in Mathematics by Platinum (122,256 points) | 66 views

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&P_{1}: x+y+z=1 \\
&P_{2}: x^{2}+y^{2}+z^{2}=2 \\
&P_{3}: x^{3}+y^{3}+z^{3}=3 \\
&P_{4}: x^{4}+y^{4}+z^{4}=? \\
&\text { Solution: } \\
&P_{1}+e_{1}=0 \Rightarrow e_{1}=-1 \\
&P_{2}+P_{1} e_{1}+2 e_{2}=0 \Rightarrow e_{2}=-\frac{1}{2} \\
&P_{3}+P_{2} e_{1}+P_{1} e_{2}+3 e_{3}=0 \Rightarrow e_{3}=-\frac{1}{6} \\
&P_{4}+P_{3} e_{1}+P_{2} e_{2}+e_{3} P_{1}=0 \Rightarrow P_{4}=\frac{25}{6} \\
&\therefore P_{4}: x^{4}+y^{4}+z^{4}=\frac{25}{6} .
by Platinum (122,256 points)

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