x=根号17-1 求x^5+2x^4-17x^3-x^2+18x-16

x=根号17-1 求x^5+2x^4-17x^3-x^2+18x-16
x=根号17-1 求x^5+2x^4-17x^3-x^2+18x-16

x=根号17-1 求x^5+2x^4-17x^3-x^2+18x-16
若x=√(17)-1,则x^5+2x^4-17x^3-x^2+18x-16的值为 0
因x=√17-1
则(x+1)^2=17
化简得 x^2+2x = 16
则
x^5+2x^4-17x^3-x^2+18x-16
= x^3(x^2+2x) -17x^3-x^2+18x-16
= 16x^3 -17x^3-x^2+18x-16
= -x^3 - x^2 +18x-16
= -x(x^2+2x) +x^2 +18x-16
= -16x +x^2+18x-16
= x^2+2x -16
= 16 -16
= 0