Solving a Root Equation for the Variable r

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The discussion focuses on rearranging the equation A = πr² + r²√(k²-1) to solve for the variable r. Participants clarify that the common factor r² can be factored out, leading to the equation r²(π + √(k²-1)) = A. The next step involves dividing both sides by (π + √(k²-1)) and then taking the square root to isolate r, resulting in r = √(A / (π + √(k²-1))). The conversation also touches on other algebraic manipulations and the importance of handling square roots and surds correctly. Overall, the thread emphasizes the process of isolating variables in algebraic equations.
  • #61
In fact, perhaps your original post contained a typo. You went from
A = πr² + r²root(k²-1) to r³ = (2A/π+root(k²-1)
Did you really mean the r³, rather than r²?
 
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  • #62
:redface: i believe your right
 

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