以知x+x^-1=3,求x^2/3+x^-2/3.再求:x^2/3-x^-2/3应该是:x^(2/3)-x^(-2/3)x^(2/3)+x^(-2/3)

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以知x+x^-1=3,求x^2/3+x^-2/3.再求:x^2/3-x^-2/3应该是:x^(2/3)-x^(-2/3)x^(2/3)+x^(-2/3)

以知x+x^-1=3,求x^2/3+x^-2/3.再求:x^2/3-x^-2/3应该是:x^(2/3)-x^(-2/3)x^(2/3)+x^(-2/3)
以知x+x^-1=3,求x^2/3+x^-2/3.
再求:x^2/3-x^-2/3
应该是:x^(2/3)-x^(-2/3)
x^(2/3)+x^(-2/3)

以知x+x^-1=3,求x^2/3+x^-2/3.再求:x^2/3-x^-2/3应该是:x^(2/3)-x^(-2/3)x^(2/3)+x^(-2/3)
因为x^2/3+x^-2/3=1/3(x^2+x^-2).且(x+x^-1)^2=x^2+x^-2+2=3^2=9,所以x^2+x^-2=7,所以x^2/3+x^-2/3=7/3.
同理,x^2/3-x^-2/3=1/3(x^2-x^-2).因为(x+x^-1)^2=x^2+x^-2+2=3^2=9
所以,(x-x^-1)^2=x^2+x^-2-2=5,所以x-x^-1=√5.又因为x^2/3-x^-2/3=1/3(x^2-x^-2)=1/3(X+1/X)(X-1/X)=3√5*1/3=√5