Bereshit 2:9 (Bereshit) – Two special trees in the Garden of Eden

Bereshit 2:9 records that G-d planted in the Garden of Eden, all types of trees, including the tree of knowledge and the tree of life. Later, 2:16,17 records that Adam could eat the fruit of all of the trees except for the fruit of the tree of knowledge. Did this permission include the fruit of the tree of life? Afterwards, 3:22 records that Adam and Havva had to leave the Garden of Eden lest they eat the fruit of the tree of life, but it was never mentioned that it was forbidden for them to eat the fruit of this tree.

The two trees would have given Adam the two elements needed to become like G-d, divine knowledge and eternity. He was never able to eat from both the fruit of both trees since he could never become like G-d. In theory, he could have eaten from either of the two trees. He could have had either eternal life or divine knowledge but not both. Thus, once he ate from the tree of knowledge, then he could no longer live forever, and he had to be banished from the Garden of Eden. Yet, I doubt Adam really could have chosen eternal life and not divine knowledge.

My guess is that initially Adam was not physically able to eat from the tree of life since it was inaccessible to him, too high. Thus, he did not have to be told not to eat from the tree. However, once he and Havva attained the divine knowledge, they could have figured out how to get to the fruit from the tree of life, but this could not be allowed, so they were banished from the garden.