己知x-1/x=-3,求xx-1/xx的值.
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己知x-1/x=-3,求xx-1/xx的值.
己知x-1/x=-3,求xx-1/xx的值.
己知x-1/x=-3,求xx-1/xx的值.
x-1/x=(x^2-1)/x=3
x^2-1/x^2=(x^4-1)/x^2=(x^2-1)(x^2+1)/x^2=3*(x^2+1)/x=3*(x+1/x)
(x-1/x)^2=x^2+1/x^2-2=9
x^2+1/x^2=11
(x+1/x)^2=x^2+1/x^2+2=13
(x+1/x)=根号13
x^2-1/x^2=正负3根号13
x-1/x=-3
(x-1/x)²=9
x²-2+1/x²=9
x²+1/x²=11
x²+2+1/x²=13
(x+1/x)²=13
x+1/x=±√13
∴x²-1/x²=(x-1/x)(x+1/x)=-3×(±√13)=±3√13
x-1/x=-3
x+1/x=±√[(x-1/x)²+4]=±√(9+4)=±√13
所以
xx-1/xx=(x-1/x)(x+1/x)=-3√13 或 =3√13
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