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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
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 Originally Posted by MATHEMATICIAN $\displaystyle x^{3}y =1$ and $\displaystyle xy^{3}=1$ What are the solution sets?
Solving for y the first equation says
$\displaystyle y = \dfrac{1}{x^3}$

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 $\pm\sqrt{\pm i}$. Thanks from topsquark Tags solve Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post gen_shao Algebra 12 November 2nd, 2014 06:11 AM

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