A B 3 B C 3 C A 3 3 A B B C C A
A b a c 3 a b c b c b c b a 3 b a c c a.
A b 3 b c 3 c a 3 3 a b b c c a. If a b c are all non zero and a b c 0 prove that a2 bc b2 ca c2 ab 3. Note that we can expand the a b 3 b c 3 and c a 3 using the special product formulas for a cube of a binomial. A b c b c a c a b expand the cubes and cancel the equal and opposite terms. A b 3 b c 3 c a 3 a b b c a b 2 a b b c b c 2 c a 3 a c a 2 2ab b 2 ab b 2 ac bc b 2 2bc c 2 c a 3 c a a 2 3ab 3b 2 ac 3bc c 2 c.
You will have 27 a b c 3 a b c then divide both sides by 3. Math x y z 0 math hence math x 3 y 3 z 3 3xyz x y z x 2 y 2 z 2 xy xz yz 0 math math x 3. If a b and c are all real positive numbers then it will be correct. To simplify the above expressions start by expanding the binomials.
Asked sep 14 2018 in class ix maths by aditya23 2 145 points polynomials. Factor out the 3 in the portion on the right. Let math a b x b c y c a z math it is obvious that.