I am the home for feathery animals. What am I?

Answer: Nest

Solution:

There are two numbers whose product added to the sum of their squares is 109, and the difference of whose squares is 24. What are the two numbers?

Answer: 5 and 7. (5)² = 25(7)² = 49(5x7)+25+49=10949-25=24

Solution:

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5 and 7.
(5)² = 25(7)² = 49(5×7)+25+49=10949-25=24

What number is missing 2 3 4 2 3 ?

Answer: 5

Solution:

Answer: 5

We get numbers 234  and 235

so  2 3 4

2 3 5

I am commonly abbreviated to H. What am I?

Answer: Hydrogen

Solution:

If I drink, I die. If I eat, I am fine. What am I?

Answer: fire

Solution:

What building has the most stories?

Answer: The library.

Solution:

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The library.