已知三角形ABC中,角A,B,C的对角分别为a,b,c,且a^4+b^4+c^4=2c^2(a^2+b^2),则角C等于

c^2=a^2+b^2-2abcosCc^4=(a^2+b^2-2abcosC)^2c^4=a^4+b^4+4a^2*b^2*(cosC)^2-4a^3*bcosC-4ab^3cosC+2a^2*b^2将c^2和c^4分别带入原式2a^4+2b^4+4a^2*b^2*(cosC)^2-4a^3*bcosC-4ab^3cosC+2a^2*b^2=2*(a^2+b^2-2abcosC)...