I will start you off...

1 A

2 B

3 F

4 D

5 A

Can you do 6?

]]>Can you please copy the question exactly as it appears?

]]>]]>

I have checked the source again. It seems to actually be: (BC + CA)(BC^2 + CA^2 - AB^2) = 2*BC*CA^2. (First term is BC not BA).

Sorry for the fault!

]]>Bob

]]>Bob

]]>I've noticed that you have been posting many AoPS problems along with their official diagrams.

Please remove them as they constitute plagiarism and cause a permanent record that students who are attempting to solve the problems will see.

Thank you.]]>

Here's my proof. I used Excel to help with layout and such.

```
I've numbered the combinations/clues to help with my notation. 'x'es in combinations denote eliminated numbers.
#11 285963 tgn3 tgp2
#10 695395 tgn2 tgp0
#9 105280 tgn3 tgp0
#8 394514 tgn3 tgp0
#7 725983 tgn3 tgp1
#6 183945 tgn3 tgp1
#5 894166 tgn2 tgp0
#4 635412 tgn3 tgp1
#3 355462 tgn2 tgp1
#2 461794 tgn1 tgp0
#1 909079 tgn1 tgp0
The following shows that none of #1's digits (9,7,0) succeed, and hence there is no solution:
9 : If #1 = 9xxxxx, xx9xxx or xxxxx9, then #2 = xxxx9x. 0,1,4,6,7 are eliminated, so #4 = x35xx2. These three numbers (3,5,2) also appear in #3...which exceeds its tgn2.
7 : If #1 = xxxx7x, then #2 = xxx7xx. 0,1,4,6,9 are eliminated; so #5 = 8xxxxx...which is less than its tgn2.
0 : If #1 = x0xxxx or xxx0xx:-
(a) If #2 = 4xxxxx or xxxxx4, then 1,6,7,9 are eliminated; so #8 = 3xx5xx...which is less than its tgn3.
(b) If #2 = x6xxxx, then 1,4,7,9 are eliminated; so #8 = 3xx5xx...which is less than its tgn3.
(c) If #2 = xx1xxx, then 4,6,7,9 are eliminated; so #5 = 8xx1xx, from which #9 = 10xx8x or 1xxx80. 5,2 are eliminated, so #8 = 3xxx1x, which is less than its tgn3.
```

Welcome to the forum.

Have a look here:

https://en.wikipedia.org/wiki/Symmetric_group

and

https://en.wikipedia.org/wiki/Alternating_group

Bob

]]>So x + c = 0 => c = -3

Here is a demo with 1/(x-3)

You can see that as x gets closer to 3 from below or above, the value of the expression gets bigger and bigger. If you plot the points the curve becomes more and more vertical as you get closer to x = 3

Bob

]]>Which is it? Have you had PEMDAS yet?

]]>14 days is nothing. Some of my threads took months to reach a conclusion, like when I had to learn carpentry first, and then teach the poster how to do vectors.

Bob

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