已知x+x^(-1)=3(x>0),求下列各式的值
2个回答
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x+x^(-1)=3, 得：x^2+x^(-2)=7
(x^(3/2)+x^(-3/2))^2
=x^3+2+x^(-3)
=[x+x^(-1)][x^2-1+x^(-2)]+2
=3x6+2
=20
所以：x^(3/2)+x^(-3/2)=√ 20=2√ 5
(x^(3/2)-x^(-3/2))^2
=x^3-2+x^(-3)
=[x+x^(-1)][x^2-1+x^(-2)]-2
=3x6-2
=16
所以：x^(3/2)-x^(-3/2)=±√ 16=±4
(x^(3/2)+x^(-3/2))^2
=x^3+2+x^(-3)
=[x+x^(-1)][x^2-1+x^(-2)]+2
=3x6+2
=20
所以：x^(3/2)+x^(-3/2)=√ 20=2√ 5
(x^(3/2)-x^(-3/2))^2
=x^3-2+x^(-3)
=[x+x^(-1)][x^2-1+x^(-2)]-2
=3x6-2
=16
所以：x^(3/2)-x^(-3/2)=±√ 16=±4
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