Math Question and Answers


Question and Answers Forum

All Questions Topic List
Others Questions
Previous in All Question Next in All Question
Previous in Others Next in Others
Question Number 57618 by tanmay.chaudhury50@gmail.com last updated on 08/Apr/19

	Answered by tanmay.chaudhury50@gmail.com last updated on 09/Apr/19
	$∣b+c a−b a∣ ∣c+a b−c b∣ ∣a+b c−a c∣ ∣b a a∣+∣b −b a∣+∣c a a∣+∣c −b a ∣ ∣c b b ∣ ∣c −c b∣ ∣a b b∣ ∣a −c b∣ ∣a c c∣ ∣a −a c∣ ∣b c c∣ ∣b −a c∣ now △=△_1 +△_2 +△_3 +△_4 △_1 =△_2 =△_3 =0 reason collumn identical △=△_4 =(−1)∣c b a∣ ∣a c b∣ ∣b a c∣ =(−1)×{c(c^2 −ab)−b(ac−b^2 )+a(a^2 −bc)} =(−1)(c^3 −abc−abc+b^3 +a^3 −abc) =3abc−a^3 −b^3 −c^3$
	$∣ b + c a - b a ∣$ $∣ c + a b - c b ∣$ $∣ a + b c - a c ∣$ $∣ b a a ∣ + ∣ b - b a ∣ + ∣ c a a ∣ + ∣ c - b a ∣$ $∣ c b b ∣ ∣ c - c b ∣ ∣ a b b ∣ ∣ a - c b ∣$ $∣ a c c ∣ ∣ a - a c ∣ ∣ b c c ∣ ∣ b - a c ∣$ $n o w △ = △_{1} + △_{2} + △_{3} + △_{4}$ $△_{1} = △_{2} = △_{3} = 0 r e a s o n c o l l u m n i d e n t i c a l$ $△ = △_{4}$ $= (- 1) ∣ c b a ∣$ $∣ a c b ∣$ $∣ b a c ∣$ $= (- 1) \times {c (c^{2} - a b) - b (a c - b^{2}) + a (a^{2} - b c)}$ $= (- 1) (c^{3} - a b c - a b c + b^{3} + a^{3} - a b c)$ $= 3 a b c - a^{3} - b^{3} - c^{3}$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum