Question 498182


{{{1/r + 2/(1- r) = 4/r^2}}} ; solve for {{{r}}}


{{{1(1- r)/r(1- r) + 2r/r(1- r) = 4/r^2}}}


{{{((1- r)+ 2r)/r(1- r) = 4/r^2}}}


{{{(1- r+ 2r)/r(1- r) = 4/r^2}}}


{{{(1+r)/r(1- r) = 4/r^2}}}....cross multiply


{{{(1+r)r^2 = 4*r(1- r)}}}


{{{r^2+r^3 = 4r- 4r^2)}}}


{{{r^2+r^3 -4r+ 4r^2=0)}}}


{{{r^3+ 5r^2-4r=0)}}}


{{{r(r^2+ 5r-4)=0)}}}

solutions:

first: {{{highlight(r=0)}}}

second and third:

{{{r^2+ 5r-4=0)}}}...use quadratic formula to solve for {{{r}}}

{{{r = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{r = (-5 +- sqrt( 5^2-4*1*(-4) ))/(2*1) }}}

{{{r = (-5 +- sqrt( 25+16 ))/2 }}}

{{{r = (-5 +- sqrt( 41 ))/2 }}}

{{{r = (-5 +- 6.4)/2 }}}


{{{r = (-5 +6.4)/2 }}}

{{{r = (1.4)/2 }}}

{{{highlight(r = 0.7) }}}

or

{{{r = (-5 -6.4)/2 }}}

{{{r = (-11.4)/2 }}}

{{{highlight(r = -5.7) }}}