Transposition problem! solve x/y=(1+r^2)/(1*r^2) for r
- Thread starter Vulcan
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D
Deleted member 4993
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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.
D
Deleted member 4993
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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.
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 \(\displaystyle \displaystyle \frac{x}{y}=\frac{1+r^2}{1\ast r^2}\), \(\displaystyle \displaystyle r=\frac{\sqrt{y}}{\sqrt{x-y}}\:\text{where}\:\sqrt{x-y}\ne 0\:\text{and}\:\sqrt{y}\ne 0\)
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!
Thanks for your help Subhotosh!