数学问题:已知x+y-z=a,xy-xz-yz=b,求x^2+y^2+z^2的值.

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2025-05-24 01:15:40
推荐回答(3个)
回答1:

x+y-z=a
(x+y-z)^2=a^2
即:x^2+y^2+z^2+2xy-2xz-2yz=a^2
x^2+y^2+z^2+2(xy-xz-yz)=a^2
x^2+y^2+z^2+2b=a^2
x^2+y^2+z^2=a^2-2b

回答2:

令t=-z
x+y+t=a,
xy+yt+tx=b
x^2+y^2+t^2=a^2-2b=x^2+y^2+z^2

回答3:

x^2+y^2+z^2+2xy+2yz+2xz-2xy-2yz-2xz
=(x+y+z)^2-2(xy+yz+xz)
=a^2-2b