Question

A farmer planted legumes and cabbage in the same field that is devoid of fertilizers. The yield from this field is better than the cabbage planted in another field without legumes. Why?

Answer 1

Because bacterium called Rhizobium lives in the roots of many leguminous plants. Rhizobium is a prokaryote which is capable of fixing nitrogen. What happens is that the plant and Rhizobium coexist in a way that benefits both species. Rhizobium lives in the root nodules of the plants and forms colonies. Rhizobium and plant are connected by protein ( which is produced when the plant is germinating)
called Lectins which binds to polysaccharides on the cell surface of bacteria.
Well as we said the plant and Rhizobium coexist. The plant supplies a living space and conditions for fixing nitrogen while the bacteria supply the plant with fixed nitrogen.
Its actually an example of 'mutualism' in which two organisms of different species live very closely together, each meeting some of other's needs.
Having this bacteria is advantage to the plants since plants cannot fix nitrogen themselves. So the soil had fertilizers as well as the roots of the plant had Rhizobium, so the plant could get Nitrogen from fertilizer as well as from fixed nitrogen provided by Rhizobium. Meaning now plant gets sufficient amount of nitrogen thus the yield in the field which has leguminous + fertilizers is higher than the plant that did not have legumes.

Extra info on process nitrogen fixation which Rhizobium does. So it fixes nitrogen with the help of enzyme Nitrogenase which catalyses conversion of N2 gas to NH4+ ion
conditions for this to happen:
-supply of hydrogen
-supply if ATP
-anaerobic conditions (absence of oxygen)
If want to know the process in details, let me know :)
Hope this helps :D