Liquid Hydrogen and Oxygen in a Solid Booster?

Liquid hydrogen and oxygen are among the best rocket fuels. Is it possible to store them in a solid booster?

When a rocket is reusable, then it doesn't need to be decomposable like the ones I proposed earlier, magnesium and glass rocket. Now the problem is the fuel. I thought about using liquid hydrogen and oxygen trapped in a casing with sections inside, like in the image shown.  After reading an article I decided a magnesium alloy can be used as the casing (Enhanced plasticity at cryogenic temperature in a magnesium alloy). Due to low temperatures, the liquid oxygen would not react with the magnesium alloy. Therefore, the encapsulated liquid fuel and the oxidizer can be stored temporarily. The inner of the booster would be a traditional rocket fuel. Once the traditional fuel is fired, it heats up the chamber and evaporates the magnesium alloy revealing the liquid fuel and the oxygen which would than react. The inner magnesium separators are used to slow down the flow of the fuel and the oxidizer. 

As a result, the goal is to use efficient liquid fuels and oxidizers in a solid booster. Enabling temporary storage of the fuel and negating the need of complex turbo pumps and fuel leaks.