若多项式A=y{x-y}{x-z}+z{x-y}{z-x},:(1)将多项式A分解因式(2) x/2=y/3=z/4,求
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若多项式A=y{x-y}{x-z}+z{x-y}{z-x},:(1)将多项式A分解因式(2) x/2=y/3=z/4,求A/(xyz)的值
要详细点的,看的懂的
要详细点的,看的懂的
A=y(x-y)(x-z)+z(x-y)(z-x)
=y(x-y)(x-z)-z(x-y)(x-z)
=(y-z)(x-y)(x-z)
令x/2=y/3=z/4=k
则x=2k,y=3k,z=4k
A/(xyz)
=(y-z)(x-y)(x-z)/(xyz)
=(3k-4k)(2k-3k)(2k-4k)/(2k*3k*4k)
=-2k^3/24k^3
=-1/12
=y(x-y)(x-z)-z(x-y)(x-z)
=(y-z)(x-y)(x-z)
令x/2=y/3=z/4=k
则x=2k,y=3k,z=4k
A/(xyz)
=(y-z)(x-y)(x-z)/(xyz)
=(3k-4k)(2k-3k)(2k-4k)/(2k*3k*4k)
=-2k^3/24k^3
=-1/12
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