Question

If a= 7+4√3 then find a³+1/a³

Answer 1

I love this question because the question setter is very intelligent, and actually helps u , not scratch ur head!

Just see what you get when you take conjugate ---  Its hard to write but  i think that you got confused with that 1/a part! multiply both the numerator and denominator with 7 - 4√3 what do you get at the denominator?????

It's "1" !! one makes our life simpler! so all you end up now is

(7+4√3)³ + (7 - 4√3)³ and now expand -- this would also cancel out a lot of irrational terms! so u would end up with a simple answer!

This may look very very simple for experts, but this question illustrates how keen these exam paper setters are!