If a4+b4+c4 = 2c2(a2+b2), prove that C = 45o or 135o.
a4 + b4 +c4 = 2c2 (a2+b2)
or, (a2+b2)2 - 2a2b2 + c4 = 2(a2+b2)c2 [a2+ b2 = (a+b)2 - 2ab]
or, (a2+b2)2 - 2(a2+b2)c2 + (c2)2 = 2a2b2
or, (a2+ b2 - c2)2 = 2a2b2
or, a2+ b2 - c2= 2 ab
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