Question

Next try your hand all these problems:

De Morgan was a mathematician who lived in the nineteenth country. He once said, “In the year x² my age was x.” In which year was De Morgan born?

Answer 1

We know that the 19^th century starts from 1800 and ends in 1899 and that there is only one perfect square number between 1800 and 1899, which is 1849.

It is given that the age of De Morgan in the year x², i.e., 1849, was x years.

∴ x² = 1849

We know that for two numbers x and y, if x² = y, then.

⇒

Now, 1849 = 43 × 43 = 43²

⇒

⇒ x = 43

So, the age of De Morgan was 43 years in 1849.

Therefore, the year De Morgan was born = 1849 − 43 = 1806.