在三角形ABC中,a^4+b^4+c^4=2c^2（a^2+b^2）,求∠c

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a^4+b^4+c^4=2c^2(a^2+b^2)
a^4+b^4+c^4+2a^2b^2-2b^2c^2-2a^2c^2=2a^2b^2
(a^2+b^2-c^2)^2=2a^2b^2
(a^2+b^2-c^2)/(ab)=√2或-√2
cos∠c=(a^2+b^2-c^2)/(2ab)=√2/2或-√2/2
即cos∠c=π/4或3π/4