SOLUTION: Find the real solutions of the equation. Use a calculator to express any solutions rounded to two decimal places. pi(1 + r)^2 = 2 + pi(1 + t)

Algebra ->  Equations -> SOLUTION: Find the real solutions of the equation. Use a calculator to express any solutions rounded to two decimal places. pi(1 + r)^2 = 2 + pi(1 + t)      Log On


   

Question 1207677: Find the real solutions of the equation. Use a calculator to express any solutions rounded to two decimal places.

pi(1 + r)^2 = 2 + pi(1 + t)
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
We do not know the value of t .

The equation
pi(1 + r)^2 = 2 + pi(1 + t)
Expand
pi%281%2B2r%2Br%5E2%29=+2%2Bpi%2Bpit

pi+%2B2pir+%2Bpir%5E2+=+2%2Bpi%2Bpit
Divide by pi
1+2r+r^2 = (2/pi) +1+t
r^2 +2r -(t+2/pi )=0
Comparing the equation with ax%5E2+%2Bbx+%2Bc=0
Here a = 1 b = 2 c = -(t+2/pi)
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

Discriminant = b%5E2-4ac++=++4%2B4%28t%2B%282%2Fpi%29%29

= 4%281%2Bt%2B%282%2Fpi%29%29

r = %28-2+%2B-+sqrt%284%281%2Bt%2B2%2Fpi%29%29%29%2F2


r = %28-2%2B-+2+sqrt%281%2Bt%2B%282%2Fpi%29%29%29%2F2


r=++%28-1%2B-+sqrt%281%2Bt%2B2%2Fpi%29%29

t = ?