已知x-y+z=0,求(x²-y²-z²)-4y²z²等于多少?
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已知x-y+z=0,求(x²-y²-z²)-4y²z²等于多少?
已知x-y+z=0,求(x²-y²-z²)-4y²z²等于多少?
已知x-y+z=0,求(x²-y²-z²)-4y²z²等于多少?
(x²-y²-z²)²-4y²z²
=(x²-y²-z²)²-(2yz)²
=(x²-y²-z²-2yz)(x²-y²-z²+2yz)
=[x²-(y+z)²](x²-y²-z²+2yz)
=[x+y+z][x-(y+z)](x²-(y²+z²-2yz))
=[x+y+z][x-y-z][x^2-(y-z)^2]
=[x+y+z]*[x-y-z](x-y+z)(x+y-z)
=0
因为x+y+z=0
所以x+y=-z x+z=-y
(x²-y²-z²)²-4y²z²
=[(x+y)(x-y)-z²]²-4y²z²
=[-z(x-y)-z²]²-4y²z²
=[-z(x-y+z)]²-4y...
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因为x+y+z=0
所以x+y=-z x+z=-y
(x²-y²-z²)²-4y²z²
=[(x+y)(x-y)-z²]²-4y²z²
=[-z(x-y)-z²]²-4y²z²
=[-z(x-y+z)]²-4y²z²
=[-z(-y-y)]²-4y²z²
=(2zy)²-4y²z²
=4y²z²-4y²z²
=0
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