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May 3rd, 2019, 11:03 PM  #1 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 901 Thanks: 61 Math Focus: सामान्य गणित  solve for x and y
$\displaystyle x^{3}y =1$ and $\displaystyle xy^{3}=1$ What are the solution sets? 
May 4th, 2019, 02:24 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,969 Thanks: 2219 
Assuming that $x$ is real, $(x,\,y) = (1,\,1)$ or $(1,\,1)$. What did you mean by "solution sets"? 
May 4th, 2019, 07:34 AM  #3  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,270 Thanks: 934 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
$\displaystyle y = \dfrac{1}{x^3}$ Putting this into the second equation: $\displaystyle x \left ( \dfrac{1}{x^3} \right )^3 = 1$ $\displaystyle \dfrac{1}{x^8} = 1$ Solving this gives the two real solutions 1 and 1. Dan  
May 5th, 2019, 03:30 AM  #4 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 901 Thanks: 61 Math Focus: सामान्य गणित 
What might be the other solution beside those real solutuons?

May 5th, 2019, 04:07 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,969 Thanks: 2219 
$(x,\,y) = (x,\,1/x^3)$, where $x = \pm i$ or $\pm\sqrt{\pm i}$.


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