Answer:
see explanation
Step-by-step explanation:
Simplify the radical
[tex]\frac{U}{\frac{1}{f}+\frac{1}{g} }[/tex]
= [tex]\frac{U}{\frac{g+f}{fg} }[/tex]
= [tex]\frac{Ufg}{g+f}[/tex]
Square both sides
T² = [tex]\frac{Ufg}{g+f}[/tex] ( multiply both sides by (g + f) )
T²(g + f) = Ufg ( distribute left side )
T²g + T²f = Ufg ← subtract Ufg from both sides
T²g - Ufg + T²f = 0 ← subtract T²f from both sides
T²g - Ufg = - T²f ← factor out g from each term on the left side
g(T² - Uf) = - T²f ← divide both sides by (T² - Uf)
g = - [tex]\frac{T^2f}{T^2-Uf}[/tex] = [tex]\frac{T^2f}{Uf-T^2}[/tex]
