Question 1207677
We do not know the value of t .


The equation
pi(1 + r)^2 = 2 + pi(1 + t)

Expand 

{{{pi(1+2r+r^2)= 2+pi+pit}}}


{{{pi +2pir +pir^2 = 2+pi+pit}}}

Divide by pi

1+2r+r^2 = (2/pi) +1+t

r^2 +2r -(t+2/pi )=0

Comparing the equation with {{{ax^2 +bx +c=0}}}

Here a = 1  b = 2  c = -(t+2/pi)

{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}


Discriminant =  {{{b^2-4ac  =  4+4(t+(2/pi))}}}


= {{{4(1+t+(2/pi))}}}


r =  {{{(-2 +- sqrt(4(1+t+2/pi)))/2}}}



r = {{{(-2+- 2 sqrt(1+t+(2/pi)))/2}}}



{{{r=  (-1+- sqrt(1+t+2/pi))}}}


t = ?