已知x²-x-1=0求x5-x4-3x3+3x2+x的值

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已知x²-x-1=0求x5-x4-3x3+3x2+x的值
已知x²-x-1=0求x5-x4-3x3+3x2+x的值

已知x²-x-1=0求x5-x4-3x3+3x2+x的值
x^2-x-1=0 --->x^2-x=1
x^5-x^4-3x^3+3x^2+x
=(x^5-x^4-x^3)-2x^3+3x^2+x
=(x^5-x^4-x^3)+(-2x^3+2x^2+2x)+x^2+x-2X
=x^3(x^2-x-1)-2x(x^2-x-1)+(x^2-x)
=0-0+1
=1
祝您学习愉快

x²-x-1=0
x5-x4-3x3+3x2+x
=x5-x4-x3-2x3+2x2+2x+x2-x
=x3(x2-x-1)-2x(x-x-1)+(x2-x-1)+1
=0+0+0+1
=1

负六

x5-x4-3x3+3x2+x
=x5-x4-x3-2x3+2x2+2x+x2-x
=x3(x2-x-1)-2x(x2-x-1)+(x2-x-1)+1
=0+0+0+1
=1

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