[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 534
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Yeah, find the extra one. More precisely, the most superfluous one (answer: mashka from all 16 in the top row).
This does not mean that I agree with the solution logic of the previous example.
Yeah, find the extra picture.
This is a task for criminal investigation officers.
Presenting a similar task for urologists)))))))))
Anyone interested...
System:
(x^2)*y+y+x*(y^2)+x=18*x*y
(x^4)*(y^2)+y^2++(x^2)*(y^4)+x^2=208*(x^2)*(y^2)
I don't have the solution.
Anyone interested...
System:
(x^2)*y+y+x*(y^2)+x=18*x*y
(x^4)*(y^2)+y^2++(x^2)*(y^4)+x^2=208*(x^2)*(y^2)
I don't have the solution.
Me neither as I don't know what that birdie is between the constant and the variable.
i.e. the answer is in the form of (x1, y1) (x2, y2) etc. Not a relationship.
If you meant to express x by y or vice versa, that would be too simple and uninteresting :)
Watched the movie "Christmas trees" yesterday. Nice Christmas comedy.
The story goes on to claim that, on average, six people are enough to make contact with anyone on the planet, the first of whom is an acquaintance of yours, the second an acquaintance of the first, and so on. This is the so-called six handshake theory.
I wonder, who can think how to formalize this problem for analytical solution? For example, let's define a two-dimensional coordinate grid - the habitat. Each node in the grid is a person... What next?
Well, let's have a go. It's Friday, after all... :)
What shall we analytically solve? We shall check and estimate reasonableness of the theory (that is easier) or we shall search concrete "friends in the sixth degree" (that is more difficult, because it is necessary to make something like a database).
??
(x^2)*y+y+x*(y^2)+x=18*x*y
(x^4)*(y^2)+y^2++(x^2)*(y^4)+x^2=208*(x^2)*(y^2)
Well, for example, here's an observation: if (x,y) is the solution, so is (y,x). The trivial solution is (0,0). This, as you can see, is the only solution in which at least one variable is zero. So we can divide the equations into different degrees of the variables - without fear of losing anything by eliminating the trivial solution.
OK, divide the first equation by xy and the second by x^2*y^2:
x + 1/x + y + 1/y = 18
x^2 + 1/x^2 + y^2 + 1/y^2 = 208
Next - substitute x + 1/x = w, y + 1/y = z, then:
w + z = 18
w^2 + z^2 = 212
Solutions of the system: (w, z) = (14, 4) or (w, z) = (4, 14). Then we return to the original variables:
x + 1/x = 4
y + 1/y = 14
or
x + 1/x = 14
y + 1/y= 4
It is easy to see that all solutions of the second system are obtained from solutions of the first system by a permutation of the type (x,y) -> (y,x). The first system has 4 solutions. So the original system has a total of 8 solutions + one trivial (0,0), i.e. 9 solutions.
If you meant to express x by y or vice versa, that would be too simple and uninteresting :)
No easier than solving the system. It's even more complicated than that.
I know it's a symmetric system. I was trying to solve it by replacing x+u=a, xu=b.
Well, now it's not interesting anymore, when it turned out to be so simple (when it's already solved).
That's ok, I've got another one... Shall I post it here later? (when I solve it or get desperate).
Shall I post it here later?