Transposition problem! solve x/y=(1+r^2)/(1*r^2) for r

[Vulcan]

Equation given is x/y=(1+r^2)/(1*r^2) being asked to solve for r and solution given is r = sqrt((x*y)/(x+y))

Try as I might, I cannot get that solution.

Can anyone help, please?

 

[Deleted member 4993]

Equation given is x/y=(1+r^2)/(1*r^2) being asked to solve for r and solution given is r = sqrt((x*y)/(x+y))

Try as I might, I cannot get that solution.

Can anyone help, please?

Does '*' mean multiplication in this problem?

Please share your work (even if you you know it is wrong) with us, so that we know where to start.

 

[Vulcan]

This is how far I got

Hope you can read this!

 

[Deleted member 4993]

Equation given is x/y=(1+r^2)/(1*r^2) being asked to solve for r and solution given is r = sqrt((x*y)/(x+y))

Try as I might, I cannot get that solution.

Can anyone help, please?

x/y=(1+r^2)/(1*r^2)

x/y=(1+r^2)/r^2

x/y=1/r^2 + 1

r^2 = y/(x-y)

r = ± √[y/(x-y)]

Unless there are more assumptions (conditions) were given, the stated "given solution" is incorrect.

 

[Vulcan]

Sorted!

 

[ksdhart2]

In order to get to the given solution, we must correct an error in the transcription. I don't know if you copied it from your book/worksheet incorrectly, or if it was given to you with the error already made. What is written here is the * symbol, meaning times, or multiplication, and what is needed for the solution to be correct is the - symbol, meaning minus, or subtraction. That is to say:

Given $\displaystyle \displaystyle \frac{x}{y}=\frac{1+r^2}{1-r^2}$, $\displaystyle \displaystyle r=\frac{\sqrt{x-y}}{\sqrt{x+y}}\:\text{where}\:\sqrt{x+y}\ne 0\:\text{and}\:y\ne 0$

Given $\displaystyle \displaystyle \frac{x}{y}=\frac{1+r^2}{1\ast r^2}$, $\displaystyle \displaystyle r=\frac{\sqrt{y}}{\sqrt{x-y}}\:\text{where}\:\sqrt{x-y}\ne 0\:\text{and}\:\sqrt{y}\ne 0$

 

[Vulcan]

In order to get to the given solution, we must correct an error in the transcription. I don't know if you copied it from your book/worksheet incorrectly, or if it was given to you with the error already made. What is written here is the * symbol, meaning times, or multiplication, and what is needed for the solution to be correct is the - symbol, meaning minus, or subtraction. That is to say:

Given $\displaystyle \displaystyle \frac{x}{y}=\frac{1+r^2}{1-r^2}$, $\displaystyle \displaystyle r=\frac{\sqrt{x-y}}{\sqrt{x+y}}\:\text{where}\:\sqrt{x+y}\ne 0\:\text{and}\:y\ne 0$

Given $\displaystyle \displaystyle \frac{x}{y}=\frac{1+r^2}{1\ast r^2}$, $\displaystyle \displaystyle r=\frac{\sqrt{y}}{\sqrt{x-y}}\:\text{where}\:\sqrt{x-y}\ne 0\:\text{and}\:\sqrt{y}\ne 0$

it was show as 1 r2 ​, I assumed as there was no operator shown that is was a multiplication. Makes sense now, I will put the minus sign in.

Thanks!

 

[Vulcan]

x/y=(1+r^2)/(1*r^2)

x/y=(1+r^2)/r^2

x/y=1/r^2 + 1

r^2 = y/(x-y)

r = ± √[y/(x-y)]

Unless there are more assumptions (conditions) were given, the stated "given solution" is incorrect.

Thanks for your help Subhotosh!