Mathematical Induction?

x1, x2, x3, ... is defined recursively by x0 = 1,

xn+1 = (3xn + √5xn2- 4 )1/2

Show that all these are integers!

12 Answers

24
eureka123 ·

any hint sir.......(small one will also help)........

62
Lokesh Verma ·

the obvious one.. prove that the number is a perfect square!

use recursion..

24
eureka123 ·

okkkkkk........i will try......

1
Philip Calvert ·

x1=3+√5-4
= 4
x2 = 12 + √5(16)-4
= 12 + √76 [7][7][7]

1
Philip Calvert ·

do u mean (5x)2

1
Philip Calvert ·

if i have done something disastrously wrong just tell me i wud go to sleep but atleast break the suspense

62
Lokesh Verma ·

i dont think i meant any of that.. this is a stupid question of the day..

62
Lokesh Verma ·

you are not wrong philip,... this question is a disastor...

now i dont remember what i was upto a couple of nights back...

trust me i dont drink ;) So i was sober when giving this question :P

24
eureka123 ·

thats why it went unanswered for so long.....................................

62
Lokesh Verma ·

now i think the question is corrected :)

11
Subash ·

im still getting x2 to be √10

please correct me

11
Anirudh Narayanan ·

WOW!!!
Such an old thread [11]

Thanx for digging it up, eureka!

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