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三元一次方程有什麼技巧
三元一次方程有什麼技巧
更新时间:2025-04-04 04:20:13

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三元一次方程有什麼技巧(這樣的高次方程)1

解法一:原方程可做如下變形

(x^2-x 1)^5-x^5 4(x^2-x 1)-4x=0

∴(x^2-x 1)^5 4(x^2-x 1)=x^5 4x

令f(t)=t^5 4t

∴f(x)=x^5 4x

f(x^2-x 1)=(x^2-x 1)^5 4(x^2-x 1)

∴f(x)=f(x^2-x 1)

∴x=x^2-x 1

∴x^2-2x 1=0

即(x-1)^2=0

∴x=1

解法二:∵x^2-x 1-x=(x-1)^2≥0

∴x^2-x 1≥x

∴(x^2-x 1)^5≥x^5

而4x^2-8x 4=(2x-2)^2≥0

∴要使原方程成立:

需滿足:x^2-x 1=x和2x-2=0

∴x=1

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