My Math Forum how old is he?

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 August 22nd, 2019, 10:21 PM #1 Newbie   Joined: Jul 2019 From: jakarta Posts: 6 Thanks: 2 how old is he? Hi fellas, I was given this puzzle in school. Here goes : Jack's great-grandfather was a mathematician. He was x years old on 26 june in the year x^2 How old was Jack's great-grandfather when he published his book, cosmic topology, on 26 June in the year 1973? my guess is x =44 and the answer to the question is 37 is it correct? I was doing trial and error using calc. what is the smart / algebraic way of solving it?
 August 22nd, 2019, 11:16 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,972 Thanks: 2222 The question is unclear... which person is being referred to as "he" in each of the places where "he" is used? If anyone was born in the year x² - x, where x² - x < 1973, x is at most 44. To conclude that x = 44, consider that if x were 43 or less, the year x² - x would be the year 1806 or earlier.
 August 22nd, 2019, 11:28 PM #3 Senior Member   Joined: Apr 2014 From: UK Posts: 965 Thanks: 342 They way I'd find the answer is to take the integer of the root of 1973 to get a starting point for his age. int((1973)^0.5) = 44 I'd then do the following: 43^2 = 1849, , born in (1849-43) 1806, he'd be 167 in 1973, not likely. 44^2 = 1936, born in (1936-44) 1892 he'd be 81 in 1973, quite possible! 45^2 = 2025, born in (2025-45) 1980, he hasn't been born yet in 1973 The last one isn't really required, since the answer will always be higher than the year that was initially rooted, but if time permits, a sanity check is always a good idea! So I make it 81.

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