[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 497

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TheXpert:
Can I have the root?

And numbers?
 

No root, but I like the idea. Like a cubic equation or something?

In short, it looks like we need to make a proper symmetric f-from these three variables.

P.S. Just got it. There is no root operation of any degree.

And digits... Well, if you need 5a, you could do, say, a+a+a+a+a.

 

Oh, it's complicated, Andrei. Where's the s?

P.S. The problem is for 8th-11th grades. No need for integrals.

 
Mathemat:

No root, but I like the idea. Like a cubic equation or something?

In short, it looks like we need to make a proper symmetric f-from these three variables.

P.S. Just got it. There is no root operation of any degree.

And digits... Well, if you need 5a, you could do, say, a+a+a+a+a.


No, you have to divide it by three.
 

In short, good equations (x2 is the desired one)

a*a + b*b + c*c = 2*x1*x1 + x2*x2
(a - b)^2 + (b - c)^2 + (a - c)^2 = 2(x1 - x2)^2
a + b + c = 2*x1 + x2
1/a + 1/b + 1/c = 2/x1 + 1/x2 = (2*x2 + x1)/(x1*x2)
 
TheXpert:

In short, good equations (x2 -- the sought after one)

I'll add:

(a-b)*(a-c) + (b-a)*(b-c) + (c-a)*(c-b) = (x1-x2)^2 = x1^2 - 2*x1*x2 + x2^2

 
You can't do it without the square root, can you?
 
TheXpert:

In short, good equations (x2 is the desired one)


something is wrong. The conditions don't mention x1 or x2.

I.e. only numbers a, b, c and arithmetic operations.

It should be:

f(a,b,c) = c

For example:

a - b + c = c

a : b * c = c

Something like this. The difficulty is that you don't know which of these 3 numbers are "the same" and which are "different", i.e. the arithmetic expression must be universal.

 
Roger:
You can't do it without the square root, can you?
So far, yes, I haven't figured it out.
 
MetaDriver:

I'll add:

(a-b)*(a-c) + (b-a)*(b-c) + (c-a)*(c-b) = (x1-x2)^2 = x1^2 - 2*x1*x2 + x2^2




somehow:

a + b + c = x1 + x1 + x2
---
x2 = a + b + c - x1 - x1 ,

где
  x1 = ( (a-b)*(a-c) + (b-a)*(b-c) + (c-a)*(c-b) ) / ( (b-a)*b/c + (c-b)*c/a + (a-c)*a/b )
1...490491492493494495496497498499500501502503504...628
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