四方+b四方+c四方=2c平方(a平方+b平方)
a^4-2c^2a^2+b^4+c^4-2c^2b^2=0
(a^2+b^2-c^2)^2=
a^4+b^4+c^4-2c^2a^2-2c^2b^2+2a^2b^2=0+2a^2b^2
所以
(a^2+b^2-c^2)^2=2a^2b^2
a^2+b^2-c^2=√2ab 或 a^2+b^2-c^2=-√2ab
cosC=a^2+b^2-c^2/2ab=√2ab/2ab=√2/2
或
cosC=-√2/2
所以C=45°或135°
四方+b四方+c四方=2c平方(a平方+b平方)
a^4-2c^2a^2+b^4+c^4-2c^2b^2=0
(a^2+b^2-c^2)^2=
a^4+b^4+c^4-2c^2a^2-2c^2b^2+2a^2b^2=0+2a^2b^2
所以
(a^2+b^2-c^2)^2=2a^2b^2
a^2+b^2-c^2=√2ab 或 a^2+b^2-c^2=-√2ab
cosC=a^2+b^2-c^2/2ab=√2ab/2ab=√2/2
或
cosC=-√2/2
所以C=45°或135°