with Q.

hello......doctor~

there does not exist "x" in rational number
such that x^2 =12.

---------------------------------------
if there exists "x" in Q,
x = n/m , (n,m)=1. n,m in Z.

so, (n/m)^2 = 12

=> n^2 = 12.m^2

so, n^2 is even => n is even.

so, n=2k form.

since n^2 = 12.m^2, (2k)^2 = 12.m^2.

=> 4k^2 = 12.m^2

=> k^2 = 3.m^2

i want to deduce that m is even and (m,n) =/= 1.
in the end, "x" does not exist by contradiction.

but i can't induce the my idea.

is this impossible work ?

i want to know a correct solution in this case.

thank you very much for your advice.


.

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