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?

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...

全部展开

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

收起