Show that α=³√(7+5√2)+³√(7-5√2) is an integer. No calculators or computers allowed!

(In reply to re: Solution by David Shin)

Hi David, your starting statement

(1+sqrt(2))^3=(7+5sqrt(2)) and (1-sqrt(2))^3=(7-5sqrt(2)) was a bit of a leap for me.  But I managed to figure out that...

7+5sqrt(2) = (3+2sqrt(2))(1+sqrt(2))

= (1+sqrt(2))^3 and then I understood.  Thanks for the help. 

Posted by Nosher on 2004-10-14 02:02:19