Question

Put three different numbers in the circles so that when you add them at the end of each line you get a square number.

Answer 1

(For Fun)

Answer 2

i dont understand how to solve this

Answer 3

X+Y = k^2
Y+Z = m^2
Z+X = n^2

Answer 4

something like that ? :)

Answer 5

no it is x+y+z=n^2

Answer 6

uhh, then its very simple right ?

9 = 1+2+6

so put 1, 2, 6 in circles lol

Answer 7

Can you show one in the way you said @ganeshie8

Answer 8

let me think a bit, it can get comlicated :|

Answer 9

cuz we need to satisfy all 3

X+Y = k^2
Y+Z = m^2
Z+X = n^2

Answer 10

sure it will more challenging.

Answer 11

0, 9, and 16.

Answer 12

u want all 3 different numbers ?

else 2, 2, 2 will work

Answer 13

oh 0,9, 16 is brilliant...

Answer 14

but it is not like the question .

Answer 15

wat do u mean

Answer 16

oh nice great amazing.

Answer 17

if u dont allow 0,
and dont allow repetition... then it gets a bit complex too..

Answer 18

Yes it is.

Answer 19

wud be a nice exercise... to try to find them analytically if possible :)

Answer 20

Since by @ganeshie8 's equations, there are 3 equations in 3 variables (X,Y,Z), then we can get solutions if we specify values for k, m, and n.
For example, if we solve for X, we have:
(X+Y)-(Y+Z)=k^2-m^2
X-Z=k^2-m^2
X+Z=n^2
2X=k^2-m^2+n^2
X=(k^2-m^2+n^2)/2
Y and Z should be the same.

Answer 21

yes @ganeshie8

Answer 22

The only problem now is if the problem specified that the numbers in the circles should be integers.
In that case, we can choose values of k, m, and n such that either
A. all of them are even
B. two of them are odd, and the last one is even
This will guarantee that X is an integer, in this case.
A similar analysis should work for Y and Z.

Answer 23

A theory .huh!!

Answer 24

real numbers is simple as can be seen, but finding integers requires analysis...

Answer 25

Thanks guys. See you again.Now have to close it.