Answer:
b = -2c ± [√(4π²c² + πA)]/π
Explanation:
A = 4πbc + πb^2
A = 4πbc + πb²
πb² + 4πbc - A = 0
Using the quadratic formula to solve this quadratic equation.
The quadratic formula for the quadratic equation, pb² + qb + r = 0, is given as
b = [-q ± √(q² - 4pr)] ÷ 2p
Comparing
πb² + 4πbc - A = 0 with pb² + qb + r = 0,
p = π
q = 4πc
r = -A
b = [-q ± √(q² - 4pr)] ÷ 2p
b = {-4πc ± √[(4πc)² - 4(π)(-A)]} ÷ 2π
b = {-4πc ± √[16π²c² + 4πA]} ÷ 2π
b = (-4πc/2π) ± {√[16π²c² + 4πA] ÷ 2π}
b = -2c ± [√(4π²c² + πA)]/π
Hope this Helps!!!