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        riddles >> medium >> ONE REAL SOLUTION
        
(Message started by: karan on Sep 4^th, 2008, 3:15am)

Title: ONE REAL SOLUTION
Post by karan on Sep 4^th, 2008, 3:15am

18 = ((1 + x)^18/x)
17 = ((1 + x)^17/x)

Subtract => 1=1+x but x can't be zero

Hence, no soln. (the soln. given in the problem is also incorrect)

Title: Re: ONE REAL SOLUTION
Post by towr on Sep 4^th, 2008, 6:04am

How do you come by 1=1+x?

((1 + x)^18/x) = (1 + x) (1 + x)^17/x
So, subtracting the second equation from the first yield
1 = (1 + x)^17

Title: Re: ONE REAL SOLUTION
Post by karan on Sep 4^th, 2008, 8:07am

same thing, 1=(1+x)^17 is same as 1=1+x

Title: Re: ONE REAL SOLUTION
Post by Grimbal on Sep 4^th, 2008, 9:51am

Anyway, plotting the function ((1+x)^18)/x shows a minimum of 47.56 at x=1/17.

Title: Re: ONE REAL SOLUTION
Post by 1337b4k4 on Sep 4^th, 2008, 12:11pm

You can also divide one by the other to get 18/17 = 1+x, a contradiction.