[Math] Find the value...
回答 (2)
2011-02-27 7:58 am
✔ 最佳答案
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2011-02-27 5:13 pm
If x + 1/x = 1，find the value of x^2048 + 1/x^2048.
Sol
x+1/x=1
x^2+1=x
x^2-x+1=0
(x+1)(x^2－x+1)=0
x^3+1=0
x^3=－1
x^2048
=x^2046*x^2
=(x^3)^682*x^2
=[(－1)^682]*x^2
=x^2
x^2048+1/x^2048
=x^2+1/x^2
=x^2+2+1/x^2－2
=(x+1/x)^2－2
=1－2
=－1
Sol
x+1/x=1
x^2+1=x
x^2-x+1=0
(x+1)(x^2－x+1)=0
x^3+1=0
x^3=－1
x^2048
=x^2046*x^2
=(x^3)^682*x^2
=[(－1)^682]*x^2
=x^2
x^2048+1/x^2048
=x^2+1/x^2
=x^2+2+1/x^2－2
=(x+1/x)^2－2
=1－2
=－1
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