Question

已知x的三次方等于负一求代数式X乘x二次方乘X的三次方......乘到X的2005次方

Answer 1

x的三次方等于负一，则x=-1

X乘x二次方乘X的三次方......乘到X的2005次方等于1003个负1与1002个正1相乘，等于负1

Answer 2

负

Answer 3

x^3=-1
x=-1
x*x^2*x^3*……*x^2005
=x^(1+2+3+……+2005)
=x^2005*1003
=(-1)^(2004*1003-1003)
=(-1)^(2*1002*1003)*(-1)^1003
=1*(-1)
=-1

Answer 4

x^3=-1,
x=-1
x*x^2*x^3*-----x^2005
=x^(1+2+3+---+2005)
=x^(1003*2005)
=-1

Answer 5

x^3=-1
x=-1

x*x^2*x^3*……*x^2005
=x^(1+2+3+……+2005)
=x^[(1+2005)*2005/2]
=x^1003*2005

1003*2005=(1002+1)*2005
=1002*2005+2005
=1002*2005+2004+1
=3*334*2005+3*668+1

所以原式=x^(3*334*2005+3*668+1)
=(x^3)^334*2005*(x^3)^668*x
=(-1)^334*2005*(-1)^668*x
334*2005和668都是偶数
所以原式=1*1*x
=-1