Question

(a²+b²-c²)-(b²+c²-a²)+(c²-a²)=a²-c² доведіть тотожність​

Answer 1

$( {a}^{2} + {b}^{2} - {c}^{2} ) - ( {b}^{2} + {c}^{2} - {a}^{2} ) + ( {c}^{2} - {a}^{2} ) = {a}^{2} - {c}^{2} \\ {a}^{2} + {b}^{2} - {c}^{2} - {b}^{2} - {c}^{2} + {a}^{2} + {c}^{2} - {a}^{2} = {a}^{2} - {c}^{2} \\ {a}^{2} + {a}^{2} - {a}^{2} + {b}^{2} - {b}^{2} - {c}^{2} - {c}^{2} + {c}^{2} = {a}^{2} - {c}^{2} \\ {a}^{2} - {c}^{2} = {a}^{2} - {c}^{2}$

Answer 2

$\Big(a^{2} +b^{2}-c^{2} \Big)-\Big(b^{2}+c^{2}-a^{2}\Big)+\Big(c^{2}-a^{2}\Big)=\\\\=a^{2} +b^{2}-c^{2}-b^{2}-c^{2}+a^{2}+c^{2}-a^{2}=a^{2}-c^{2}\\\\\boxed{a^{2}-c^{2} =a^{2}-c^{2} }$

Тождество доказано