已知:1995x^3=1996y^3=1997z^3xyz>0(1995x^2+1996y^2+1997z^2)的立方根=1995的立方根+1996的立方根+1997的立方根求:1/x+1/y+1/z的值
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![已知:1995x^3=1996y^3=1997z^3xyz>0(1995x^2+1996y^2+1997z^2)的立方根=1995的立方根+1996的立方根+1997的立方根求:1/x+1/y+1/z的值](/uploads/image/z/6879454-70-4.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9A1995x%5E3%3D1996y%5E3%3D1997z%5E3xyz%3E0%281995x%5E2%2B1996y%5E2%2B1997z%5E2%29%E7%9A%84%E7%AB%8B%E6%96%B9%E6%A0%B9%3D1995%E7%9A%84%E7%AB%8B%E6%96%B9%E6%A0%B9%2B1996%E7%9A%84%E7%AB%8B%E6%96%B9%E6%A0%B9%2B1997%E7%9A%84%E7%AB%8B%E6%96%B9%E6%A0%B9%E6%B1%82%EF%BC%9A1%2Fx%2B1%2Fy%2B1%2Fz%E7%9A%84%E5%80%BC)
已知:1995x^3=1996y^3=1997z^3xyz>0(1995x^2+1996y^2+1997z^2)的立方根=1995的立方根+1996的立方根+1997的立方根求:1/x+1/y+1/z的值
已知:
1995x^3=1996y^3=1997z^3
xyz>0
(1995x^2+1996y^2+1997z^2)的立方根=1995的立方根+1996的立方根+1997的立方根
求:
1/x+1/y+1/z的值
已知:1995x^3=1996y^3=1997z^3xyz>0(1995x^2+1996y^2+1997z^2)的立方根=1995的立方根+1996的立方根+1997的立方根求:1/x+1/y+1/z的值
1995x^3=1996y^3=1997z^3=k^3
1995x^2=k^3/x,1996y^2=k^3/y,1997z^2=k^3/z
(1995x^2+1996y^2+1997z^2)的立方根
=(k^3/x+k^3/y+k^3/z)的立方根
1995x^3=1996y^3=1997z^3=k^3
1995=k^3/x^3,1996=k^3/y^3,1997=k^3/z^3
1995的立方根+1996的立方根+1997的立方根
=k/x+k/y+k/z
(1995x^2+1996y^2+1997z^2)的立方根=1995的立方根+1996的立方根+1997的立方根
(k^3/x+k^3/y+k^3/z)的立方根=k/x+k/y+k/z
(1/x+1/y+1/z)的立方根=1/x+1/y+1/z
1/x+1/y+1/z=(1/x+1/y+1/z)^3
(1/x+1/y+1/z)[(1/x+1/y+1/z)^2-1]=0
因为xyz>0
所以1/x+1/y+1/z=1
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