work out vs strengthen

work out and strengthen both are verbs.

Word	Noun	Adjective	Verb	Adverb
work out	No	No	Yes	No
strengthen	No	No	Yes	No

As verbs, strengthen is a hyponym of work out; that is, strengthen is a word with a more specific, narrower meaning than work out:

Other hyponyms of work out include limber up, loosen up, warm up, train, tumble, tone, tone up, press, weight-lift, weightlift.

work out (verb)	strengthen (verb)
do physical exercise	give a healthy elasticity to
give a workout to	gain strength
come up with	make strong or stronger
work out in detail
find the solution to (a problem or question) or understand the meaning of
make a mathematical calculation or computation
be calculated
happen in a certain way, leading to, producing, or resulting in a certain outcome, often well