Q:

Book about a dying planet that prohibited marriage between the 3 races living on the planet

Looking for a book title about a dying planet that prohibited marriage between the 3 races, they found that intermarriage produced a new race of engineers that they had been missing and could solve their problems. 

A:

The Gods Themselves (1972) by Asimov?  It was the answer to 1970s novel, planetary world with 3 gender species, prohibited inter-species procreation, a very similar question that was asked yesterday:

Prohibited inter-species procreation - eventually allowed, producing 4th gender.  Two of the three genders are bureaucrats, thinkers/builders. 

From Wikipedia:

The main plot-line is a project by those who inhabit a parallel universe (the para-Universe) with different physical laws from this one.  By exchanging matter from their universe—para-Universe—with our universe, they seek to exploit the differences in physical laws.  The exchange of matter provides an alternative source of energy to maintain their universe.  However, the exchange will likely result in the collapse of the Earth's Sun into a supernova, and possibly even turning a large part of the Milky Way into a quasar.  There is hope among those in the para-Universe that the energy explosion does happen in our universe. 

About the three races:

The inhabitants are divided into dominant "hard ones" and subject "soft ones".  The latter have three sexes with fixed roles for each sex:

Rationals (or "lefts") are the logical and scientific sex; identified with masculine pronouns and producing a form of sperm.  They have limited ability to pass through other bodies. 

Emotionals (or "mids") are the intuitive sex; identified with the feminine pronouns and provide the energy needed for reproduction.  Emotionals can pass freely in and out of solid material, including rock. 

Parentals (or "rights") bear and raise the offspring, and are identified with masculine pronouns.  Parentals have almost no ability to blend their bodies with others, except when helped by one or both of the other sexes. 

It's later described that the union of these separate groups lead to a "scientist", who could be your engineer:

Odeen convinces Dua that the hard one they will become will have influence with the others to stop the Pump; but as their final metamorphosis (the true meaning of "passing on") begins, Dua realizes (too late to prevent irreversible union) that her own triad's "hard" form is the scientist Estwald. 

Estwald being the man behind the Pump, which allows transfer of matter between universes. ( Though it's actually more the problem than the solution)

