China Can you solve this Math Olympiad

Math Olympiad Question
Maths Olympiads are held all around the world to Recognise students who excel in Maths. The test is
offered at many grade levels and provides them with numerous possibilities to win certifications,
awards, and even scholarships for higher studies.
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China Can you solve this Math Olympiad

[@MrSeezero]

If one simply uses some common sense when trying to solve this problem, this is a relatively easy problem to solve. First, you can find out that a = b = c by setting the three sums equal to each other. Once you find that out, you can convert any of these equations to 2a = a^3. The rest is also easy.

[@bennybro6418]

BTW a=b=c=0 would be ok as well, anyway:
a=abc-b & c=abc-b so a=c, b=abc-c & a=abc-c so b=a=c, you DO NOT need 160 seconds for that.
Now back to a+b=abc: Now that's 2a=a^3, that's 2=a^2, so ±√2=a=b=c. That really doesn't take 5 minutes.

[@agon19]

I admit the slowness of the video was a tad annoying, but he's clearly slowing it down for a wider audience.
Also, I think your solution is lacking because it doesn't lead to 0 as a possible result. When you divided both sides of the equation by 'a', you assumed that 'a' can't be 0. (Because division by 0 is undefined)

[@bennybro6418]

@@agon19 ...You read the very 1rst sentence?

[@agon19]

@@bennybro6418 well if you decide that 'a' can be 0, then you can't divide by 'a'

[@bennybro6418]

​@@agon19 Well, FIRST CASE: 0+0=0*0*0. NEXT Case AFTER 1st case: a is NOT zero and - wow! - b is NOT zero and - who would have thought that: - c is NOT zero:
a=abc-b & c=abc-b so a=c, b=abc-c & a=abc-c so b=a=c, you DO NOT need 160 seconds for that.
Now back to a+b=abc: Now that's 2a=a^3, that's 2=a^2, so ±√2=a=b=c. That really doesn't take 5 minutes.
What's your FUCKING PROBLEM?

[@javidmirab3492]

Excellent

[@reef2005]

Think of a, b & c as the sides of a cube. The sum of any 2 sides equals the volume abc which implies that a=b=c. Hence a^2=2.

[@user-wm5od9xj5i]

Great

[@user-td2gn1gi7d]

2(a +b + c ) = 3(abc) .a = b = c = 1/2 abc

[@user-id1nm3wc2e]

Its good

[@javidmirab-jo6hi]

❤❤