在三角形ABC中,已知a^4+b^4+c^4=2c^2(a^2+b^2),则∠C=?

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a^4+b^4+c^4=2c^2(a^2+b^2)
a^2=xb^2=yc^2=z2xy+xx+yy+zz=2z(x+y)+2xy
(x+y)^2-2z(x+y)+z^2=2xy
(x+y-z)^2=2xy
(aa+bb-cc)^2=2(ab)^2
(aa+bb-cc-√2ab)(aa+bb-cc＋√2ab)＝0
cc＝aa+bb-2abcosC
2cosC＝-√2或√2
C＝135度或45度