SOLUTION: Your cousin was born in the 20th century. He's x years old in the year x^2. in what year was your cousin born.

    

Since he will be x in the year x², then

the year he was born is x²-x

Since that was in the twentieth century, we have the inequality:





 and 
 
Solve each inequality separately:

Solving the first inequality:





Get critical numbers by solving















We need consider only positive numbers
for somebody's age, so we'll use the + 
only.




We use test value 44 




That's false
We test value 45 




That's true so

 and since x is an integer,



-----------------

Solve the second inequality





Get critical numbers by solving















Again, we need consider only positive numbers
for somebody's age, so we'll use the + 
only.








That is true.

We use test value 46 







That is false.

So  and since x is an integer,



So the inequality is 



Therefore x=45, and he will be 45 in the year 45² = 2025.

So he was born in the year x²-x or 45²-45 = = 2025-45 = 1980.

[At present he is 34 years old.  So if you know anybody who is 34
years old, you can tell them that they will be x in the year x² :)  ]

Edwin