作业帮已知x=根号2-1,计算x^10+2x^9-2x^8-2x^7+x^6+3x^2+5x+1的值
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/04/27 13:13:11
已知x=根号2-1,计算x^10+2x^9-2x^8-2x^7+x^6+3x^2+5x+1的值
已知x=(根号2)-1，计算x^10+2x^9-2x^8-2x^7+x^6+3x^2+5x+1的值，请写出具体过程，
已知x=(根号2)-1，计算x^10+2x^9-2x^8-2x^7+x^6+3x^2+5x+1的值，请写出具体过程，
x^10+2x^9-2x^8-2x^7+x^6+3x^2+5x+1
=x^10+x^9＋x^9-x^8-x^8-x^7-x^7+x^6+3x^2+5x+1
=(x^10+x^9)＋(x^9-x^8)-(x^8+x^7)-(x^7-x^6)+3x^2+5x+1
=x^9(x+1)+x^8(x-1)-x^7(x+1)-x^6(x-1)+3x^2+5x+1
=x^9(根号2)+x^8(根号2-2)-x^7(根号2)-x^6(根号2-2)+3x^2+5x+1
=x^8[(根号2-1)(根号2)+根号2-2]-x^6[(根号2-1)(根号2)+根号2-2]+3x^2+5x+1
=3x^2+5x+1
=5-根号2
=x^10+x^9＋x^9-x^8-x^8-x^7-x^7+x^6+3x^2+5x+1
=(x^10+x^9)＋(x^9-x^8)-(x^8+x^7)-(x^7-x^6)+3x^2+5x+1
=x^9(x+1)+x^8(x-1)-x^7(x+1)-x^6(x-1)+3x^2+5x+1
=x^9(根号2)+x^8(根号2-2)-x^7(根号2)-x^6(根号2-2)+3x^2+5x+1
=x^8[(根号2-1)(根号2)+根号2-2]-x^6[(根号2-1)(根号2)+根号2-2]+3x^2+5x+1
=3x^2+5x+1
=5-根号2
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