已知x²-3x=-1,求
1.x+1/x2.x²+1/x²3.x³+1/x³4.x^4+1/x^45.(x-1/x)²...
1.x+1/x 2.x²+1/x² 3.x³+1/x³ 4.x^4+1/x^4 5.(x-1/x)²
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x²-3x=-1
x-3=-1/x
x+1/x=3
1.x+1/x =3
2.x²+1/x²
=(x+1/x)^2-2
=3^2-2
=7
3.x³+1/x³
=(x+1/x)(x^2-1+1/x^2)
=3*(7-1)
=18
4.x^4+1/x^4
=(x^2+1/x^2)^2-2
=7^2-2
=47
5.(x-1/x)²
=x^2-2+1/x^2
=7-2
=5
x-3=-1/x
x+1/x=3
1.x+1/x =3
2.x²+1/x²
=(x+1/x)^2-2
=3^2-2
=7
3.x³+1/x³
=(x+1/x)(x^2-1+1/x^2)
=3*(7-1)
=18
4.x^4+1/x^4
=(x^2+1/x^2)^2-2
=7^2-2
=47
5.(x-1/x)²
=x^2-2+1/x^2
=7-2
=5
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已知x²-3x=-1
则x-3= -1/x
x+1/x=3
1.x+1/x=3
2.x²+1/x²
=(x+1/x)^2-2
=3^2-2
=7
3.x³+1/x³
=(x+1/x)^3-3*x*1/x*(1+1/x)
=3^3-3*3
=27-9
=18
4.x^4+1/x^4
=(x^2+1/x^2)^2-2
=7^2-2
=47
5.(x-1/x)²
=(x+1/x)^2-4
=3^2-4
=5
则x-3= -1/x
x+1/x=3
1.x+1/x=3
2.x²+1/x²
=(x+1/x)^2-2
=3^2-2
=7
3.x³+1/x³
=(x+1/x)^3-3*x*1/x*(1+1/x)
=3^3-3*3
=27-9
=18
4.x^4+1/x^4
=(x^2+1/x^2)^2-2
=7^2-2
=47
5.(x-1/x)²
=(x+1/x)^2-4
=3^2-4
=5
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