并仿照解决问题:已知x2-2x-3=0,求x3+x2-9x-8的值.
问题描述:
并仿照解决问题:已知x2-2x-3=0,求x3+x2-9x-8的值.
并仿照解决问题:已知x2-2x-3=0,求x3+x2-9x-8的值.
∵x2-2x-3=0,∴x2=2x+3
∴x3+x2-9x-8=x·x2+x2-9x-8=x·(2x+3)+(2x+3)-9x-8
=2x2+3x+2x+3-9x-8=2(2x+3)-4x-5=1
请你仿照上题的做法完成:已知x2-5x+1=0,求x3-4x2-4x-1的值.
答
∵x²-5x+1=0∴x²=5x-1∴x³-4x²-4x-1=x.x²-4x²-4x-1=x(5x-1)-4(5x-1)-4x-1=5x²-x-4(5x-1)-4x-1=5(5x-1)-x-4(5x-1)-4x-1=5x-1-5x-1=-2