Important Maths Formulas
If a^2b^2c^2abbcca=0 then prove that a=b=c a² b² c² = ab bc ca On multiplying both sides by '2', it becomes 2 ( a² b² c² ) = 2 ( ab bc ca) 2a² 2b² 2c² = 2ab 2bc 2ca a² a² b² b² c² c² – 2ab – 2bc – 2ca = 0 a² b² – 2ab b² c² – 2bc c² a² – 2ca = 0 Multiply both sides with 2, we get 2 ( a2 b2 c2 – ab – bc – ca) = 0 ⇒ 2a2 2b2 2c2 – 2ab – 2bc – 2ca = 0 ⇒ (a2 – 2ab b2) (b2 – 2bc c2) (c2 – 2ca a2) = 0 ⇒ (a –b)2 (b – c)2 (c – a)2 = 0 Since the sum of square is zero then each term should be zero ⇒ (a –b)2 = 0, (b – c)2 = 0, (c – a)2 = 0
