+0  
 
+5
1061
8
avatar+42 

How to solve this equation system:

 

sqrt(x)^sqrt(y)=9

sqrt(y)^sqrt(x)=8

 

x=?

y=?

 

Source

 Jul 17, 2016

Best Answer 

 #6
avatar+33615 
+15

Or, if you prefer, I replaced sqrt(x) by u and sqrt(y) by v, found the values of u an v (by inspection - i.e. guesswork!), then squared the resulting values to get x and y.

 Jul 18, 2016
 #1
avatar
+10

Looks like you made this one up! No solution in sight!!!!

 Jul 17, 2016
 #2
avatar+33615 
+10

x = 9

 

y = 4

 Jul 17, 2016
 #3
avatar+42 
+10

Alan, What are the steps? I mean please give the steps on how did you get those answer.

 

Thanks

Aimal  Jul 18, 2016
 #5
avatar+33615 
+15

I just did it by inspection.

 

It was fairly obvious that 3^2 = 9 and 2^3 = 8

 

From this it is clear that x = 3^2 and y = 2^2

Alan  Jul 18, 2016
 #6
avatar+33615 
+15
Best Answer

Or, if you prefer, I replaced sqrt(x) by u and sqrt(y) by v, found the values of u an v (by inspection - i.e. guesswork!), then squared the resulting values to get x and y.

Alan  Jul 18, 2016
 #4
avatar
+15

In these types of equations, there is no DIRECT solution, but iteration and interpolation methods are used, such as Newton-Raphson method. It is basically "trial and error" method.

 Jul 18, 2016
 #7
avatar+42 
0

Can you solve it using Raphson method?

Aimal  Jul 19, 2016
 #8
avatar+33615 
0

If you insist on a formal numerical method here's one way of doing it:

 

NR

but this is a very heavy-handed way to solve such a simple problem!

Alan  Jul 19, 2016

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