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viniterranova
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Find the value of x and y in this system of equations. x^y=1/y^2 and y^x=1/sqrt(x).
 one year ago
 one year ago
viniterranova Group Title
Find the value of x and y in this system of equations. x^y=1/y^2 and y^x=1/sqrt(x).
 one year ago
 one year ago

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sriramkumar Group TitleBest ResponseYou've already chosen the best response.0
\[x ^{y}=1\div y ^{2} and y ^{x}=1/\sqrt{x} \] u mean??
 one year ago

estudier Group TitleBest ResponseYou've already chosen the best response.0
From the second one, can I say that y^2 = 1/sqrt2...
 one year ago

viniterranova Group TitleBest ResponseYou've already chosen the best response.0
ok. Keep going.
 one year ago

viniterranova Group TitleBest ResponseYou've already chosen the best response.0
It´s right.
 one year ago

estudier Group TitleBest ResponseYou've already chosen the best response.0
So that gives you y and you can sub in the first to get x...
 one year ago

viniterranova Group TitleBest ResponseYou've already chosen the best response.0
I solved this question before, but i can´t remember all the steps.
 one year ago

viniterranova Group TitleBest ResponseYou've already chosen the best response.0
May you show me, how?
 one year ago

ash2326 Group TitleBest ResponseYou've already chosen the best response.2
@viniterranova Let's continue, would you mind showing me your work?
 one year ago

ujjwal Group TitleBest ResponseYou've already chosen the best response.0
From the second i can say that y=1
 one year ago

viniterranova Group TitleBest ResponseYou've already chosen the best response.0
I mad x^y = y.
 one year ago

viniterranova Group TitleBest ResponseYou've already chosen the best response.0
So, if x^y=y I got the following expression. y= 1/y^2.
 one year ago

ujjwal Group TitleBest ResponseYou've already chosen the best response.0
I don't know how you got these.. But i am sure they (your above expressions) will still give correct answer since i get y=1 from 2nd expression!!
 one year ago

ash2326 Group TitleBest ResponseYou've already chosen the best response.2
I know you are substituting but don't use the same variable \[x^y=y\] This will be troublesome, use another variable, if you want to but I don't see how it'd help @viniterranova
 one year ago

viniterranova Group TitleBest ResponseYou've already chosen the best response.0
Thanks ash2326.
 one year ago

viniterranova Group TitleBest ResponseYou've already chosen the best response.0
If I mad x^y=y, and rewriting the expressoin, i can got y1/y^2=0. What do they think?
 one year ago

ash2326 Group TitleBest ResponseYou've already chosen the best response.2
How could you use the same variable "y"? it's defined differently. I have something. Let me show you
 one year ago

ash2326 Group TitleBest ResponseYou've already chosen the best response.2
\[x^y=\frac{1}{y^2}\] \[y^x=\frac{1}{\sqrt x}\] Take log both sides, for both the equations \[y\log x=2\log y\] \[x\log y=\frac 1 2\log x\] multiply both the equations, we would get \[xy\log x \times \log y=\log x \times\log y\] or \[xy=1\] We have the equation \[y\log x=2\log y\] put x=1/y \[y\log{\frac 1y}=2\log y\] we get \[y\times ( \log y)=2\log y\] \[y=2\] so \[x=\frac 12\]
 one year ago

ash2326 Group TitleBest ResponseYou've already chosen the best response.2
@viniterranova do you get this?
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
\[y\times ( \log y)=2\log y\]gives y=1 and y=2 
 one year ago

ash2326 Group TitleBest ResponseYou've already chosen the best response.2
Yes @mukushla I missed that then y=1 and x=1
 one year ago

viniterranova Group TitleBest ResponseYou've already chosen the best response.0
Great.
 one year ago

viniterranova Group TitleBest ResponseYou've already chosen the best response.0
It´s rigth.
 one year ago

viniterranova Group TitleBest ResponseYou've already chosen the best response.0
I got y=1 and x= 1 in another way.
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.0
i think x=1/2 and y=2 from xy=1 if x=1/2 then y/2=1 y=2 ans
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.0
from y log x =2log y sub x=1/y y log(1/y)=2log y y(log y)=2log y dividing both sides by log y gives y=2log y/(log y) y=2 ans..... and from xy=1 2x=1 then x=1/2 ans ....
 one year ago

viniterranova Group TitleBest ResponseYou've already chosen the best response.0
Thanks everyone for the help.
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.0
ok yw, have fun....
 one year ago
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