Question

Ab - ac = bc - ba = ca - cb возможно ли, что числа a, b и c различны?

Answer 1

Нет.проверить это можно, подставив любые различные числа к примеру а=5, b=10,c=15.
получим
5×10-5×15=10×15-10×5=15×5-15×10
50-75=150-50=75-150
-15=100=-75
они не равны значит а, б и ц не могут быть различными

Answer 2

Let's analyze the given equations:

1. Ab - ac = bc - ba
2. bc - ba = ca - cb
3. ca - cb = Ab - ac

Now, let's simplify each equation step by step:

1. Ab - ac = bc - ba Factor out common terms: a(b - c) = b(c - a) Divide both sides by (b - c) (assuming b ≠ c): a = b

2. bc - ba = ca - cb Factor out common terms: b(c - a) = c(a - b) Divide both sides by (c - a) (assuming c ≠ a): b = c

3. ca - cb = Ab - ac Factor out common terms: c(a - b) = a(b - c) Divide both sides by (a - b) (assuming a ≠ b): c = a

Based on the analysis of the equations, we can see that the only way for the equations to hold true is if a = b = c. So, it is not possible for a, b, and c to be distinct numbers if these equations are satisfied simultaneously.