已知x为实数,x^2+1/x^2=3,则x^3+1/x^3的值是

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已知x为实数,x^2+1/x^2=3,则x^3+1/x^3的值是已知x为实数,x^2+1/x^2=3,则x^3+1/x^3的值是已知x为实数,x^2+1/x^2=3,则x^3+1/x^3的值是∵x^2

已知x为实数,x^2+1/x^2=3,则x^3+1/x^3的值是
已知x为实数,x^2+1/x^2=3,则x^3+1/x^3的值是

已知x为实数,x^2+1/x^2=3,则x^3+1/x^3的值是
∵x^2+1/x^2=3
∴(x+1/x)^2
=x^2+1/x^2+2
=3+2
=5
∴x+1/x=±√5
∵x^3+1/x^3
=(x+1/x)(x^2+1/x^2-1)
=2(x+1/x)
=±2√5