Respuesta :

mhanifa

Answer:

x=0, y=0

x=2, y=4

Step-by-step explanation:

  • x^y= y^x
  • y= 2x

  • x^(2x)= (2x)^x
  • (x^2)^x= (2x)^x
  • x^2=2x
  • x(x-2)=0
  • x=0 ⇒ y=0
  • x=2 ⇒ y=4

Answer:

x = 2, y = 4.

Step-by-step explanation:

x^y = y^x

Substitute y = 2x in the above:

x^2x = (2x)^x

x^2x = 2*x * x^x      Divide both sides by x^x:

x^2x / x^x = 2*x

x^(2x-x) = 2^x

x^x = 2^x

So x = 2.

and y = 2x = 4.

We can also make x = 0 and y = 0  but

I'm not sure if  this result is valid because 0^0 is undefined.

Looking further into this there seems to be different opinions on this with some mathematicians say 0^0 = 1, so x=0, y = 0 may be acceptable.

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