Question

设x=16/√17+1，求代数式x^5+2x^4-17x^3-x^2+18x-17的值

速度………………………………

Answer 1

x=16(√17-1)/(√17-1)(√17+1)=√17-1
x+1=√17
平方
x²+2x+1=17
x²+2x=16

原式=x^3(x²+2x)-17x^3-x²+18x-17
=16x^3-17x^3-x²+18x-17
=-x^3-x²+18x-17
=-x^3-2x²+x²+18x-17
=-x(x²+2x)+x²+18x-17
=-x*16+x²+18x-17
=x²+2x-17
=16-17
=-1

Answer 2

x=16/√17+1=√17-1
则(x+1)^2=17
化简得 x^2+2x = 16
原式=x^3(x2+2x)-17x^3-x2+18x-17
=16x^3-17x^3-x2+18x-17
=-x^3-x2+18x-17
=-x^3-2x2+x2+18x-17
=-x(x2+2x)+x2+18x-17
=-x*16+x2+18x-17
=x2+2x-17
=16-17
=-1

Answer 3

x=16/√17+1=√17-1

则(x+1)^2=17
化简得 x^2+2x = 16
x^5+2x^4-17x^3-x^2+18x-16

= x^3(x^2+2x) -17x^3-x^2+18x-17

= 16x^3 -17x^3-x^2+18x-17

= -x^3 - x^2 +18x-17

= -x(x^2+2x) +x^2 +18x-17

= -16x +x^2+18x-17

= x^2+2x -17

= 16 -17

= -1

Answer 4

1.x=16(√17-1)/(√17-1)(√17+1)=√17-1
x+1=√17
平方
x²+2x+1=17
x²+2x=16

原式=x^3(x²+2x)-17x^3-x²+18x-17
=16x^3-17x^3-x²+18x-17
=-x^3-x²+18x-17
=-x^3-2x²+x²+18x-17
=-x(x²+2x)+x²+18x-17
=-x*16+x²+18x-17
=x²+2x-17
=16-17
=-1 =-1
采纳！采纳！

Answer 5

则(x+1)^2=17
化简得 x^2+2x = 16
x^5+2x^4-17x^3-x^2+18x-16

= x^3(x^2+2x) -17x^3-x^2+18x-17

= 16x^3 -17x^3-x^2+18x-17

= -x^3 - x^2 +18x-1
= -x(x^2+2x) +x^2 +18x-17

= -16x +x^2+18x-17

= x^2+2x -17

= 16 -17

= -1