Question

R + r = 2R/√3 , solve for R/r

Answer 1

    R+r = 2R/√3
or,2R =R√3+r√3
or,2R - R√3 =r√3
or,R(2-√3) =r√3
or,R/r = √3/(2-√3)
          = √3*√3/2-√3*√3
          = 3 / 2-3
          = 3/-1
  so the ans is R/r = 3/-1

Answer 2

Hi ,

R + r = 2R/√3

r = 2R/√3 - R

r = R( 2 /√3 - 1 )

r /R = ( 2 - √3 ) / √3

R/r = √3 / ( 2 - √3 )

R/r = √3( 2 + √3 ) / [ (2 - √3 )(2 + √3 )

R / r = √3 ( 2 + √3 ) / [ 4 - 3 ]

R/r = √3 ( 2 + √3 )

I hope this helps you.

:)