Two soap bubbles of radii a and b coalesce to form a single bubble of radius c. If the external pressure is P, show that the surface tension T is given by `T = P(c^(3) - a^(3) - b^(3))/(4(a^(2) + b^(2) - c^(2))`

Explanation

To solve the problem of two soap bubbles of radii \( a \) and \( b \) coalescing to form a single bubble of radius \( c \), we will use the concepts of pressure inside the bubbles and the principle of conservation of volume.

### Step-by-Step Solution:

1. **Understanding the Pressure Inside the Bubbles:**
The pressure inside a soap bubble is given by the formula:
\[
P_{\text{bubble}} = P + \frac{4T}{r}
...