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Last edited by hbghlyj 2020-2-12 10:34(1)给定非零实数A,解方程组\[\left\{ \begin{gathered}
(x - y)(y + z) = 1 - {A^2} \hfill \\
(y - z)(x + z) = - 1 - \frac{1}{{{A^2}}} \hfill \\
(z - x)(x + y) = - 1 \hfill \\
\end{gathered} \right.\]
机器解出$(x,y,z)=\left( {0,A, - \frac{1}{A}} \right)\left( {0, - A,\frac{1}{A}} \right)\left( {\frac{{{A^3} + A - 1}}{{2A\sqrt {{A^2} + A + 1} }}, - \frac{{{A^3} - A - 1}}{{2A\sqrt {{A^2} + A + 1} }}, - \frac{{{A^3} + 2{A^2} + A + 1}}{{2A\sqrt {{A^2} + A + 1} }}} \right)\left( { - \frac{{{A^3} + A - 1}}{{2A\sqrt {{A^2} + A + 1} }},\frac{{{A^3} - A - 1}}{{2A\sqrt {{A^2} + A + 1} }},\frac{{{A^3} + 2{A^2} + A + 1}}{{2A\sqrt {{A^2} + A + 1} }}} \right)\left( {\frac{{{A^3} + A + 1}}{{2A\sqrt {{A^2} - A + 1} }}, - \frac{{{A^3} - A + 1}}{{2A\sqrt {{A^2} - A + 1} }}, - \frac{{{A^3} - 2{A^2} + A - 1}}{{2A\sqrt {{A^2} - A + 1} }}} \right)\left( { - \frac{{{A^3} + A + 1}}{{2A\sqrt {{A^2} - A + 1} }},\frac{{{A^3} - A + 1}}{{2A\sqrt {{A^2} - A + 1} }},\frac{{{A^3} - 2{A^2} + A - 1}}{{2A\sqrt {{A^2} - A + 1} }}} \right)$
(2)给定$\ge2$的整数n,正数A,解方程组$x_1^i+x_2^i+\cdots+x_n^i=A,i=1,2,\cdots,n$
(3)给定$\ge2$的整数n,正数A,解方程组$x_1^i+x_2^i+\cdots+x_n^i=A^i,i=1,2,\cdots,n$ |
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