SOLUTION: Solve for r. S = (a^2)/(1 - sqrt{r^4})

Algebra ->  Equations -> SOLUTION: Solve for r. S = (a^2)/(1 - sqrt{r^4})       Log On


   

Question 1208664: Solve for r.

S = (a^2)/(1 - sqrt{r^4})
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Note that
sqrt%28r%5E4%29+=+%28r%5E4%29%5E%281%2F2%29%5E%22%22+=+r%5E%284%2A%281%2F2%29%29+=+r%5E2

So we can say,
S+=+%28a%5E2%29%2F%281+-+sqrt%28r%5E4%29%29

S+=+%28a%5E2%29%2F%281+-+r%5E2%29

S%281-r%5E2%29+=+a%5E2

S-S%2Ar%5E2+=+a%5E2

Sr%5E2+=+S-a%5E2

r%5E2+=+%28S-a%5E2%29%2FS

r+=+%22%22%2B-sqrt%28%28S-a%5E2%29%2FS%29

In other words,
r+=+sqrt%28%28S-a%5E2%29%2FS%29 or r+=+-sqrt%28%28S-a%5E2%29%2FS%29