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        riddles >> putnam exam (pure math) >> Stuck on a radical
        
(Message started by: TruthlessHero on Dec 2^nd, 2007, 2:04pm)

Title: Stuck on a radical
Post by TruthlessHero on Dec 2^nd, 2007, 2:04pm

http://www.teamserenity.com/problem.jpg

Book says it's -1/6, but I keep getting either -4/3 or -9/3.

Any advice? I've done dozens of similar problems and gotten them all right...

Err yeah - the equation = 0... Not sure how I forgot to put that in the image :o

Title: Re: Stuck on a radical
Post by pex on Dec 2^nd, 2007, 2:46pm

Are you sure you copied everything correctly? As it stands, you have 2*sqrt(-x+1) - sqrt(2x-5) = 0. I can see neither of the solutions you mention as valid, but I find x = 3/2 as the only solution.

Title: Re: Stuck on a radical
Post by towr on Dec 2^nd, 2007, 2:50pm

http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2x - 5) isn't real for x < 2.5 and 2http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(-x+1) isn't real for x > 1
So to end up as zero, I'd say they both need to have an imaginary part (because they can't be real at the same time) and so 1 < x < 2.5
Which means, I can't find myself in any of the three suggestions.

[edit]I find pex's 3/2 quite agreeable[/edit]

Title: Re: Stuck on a radical
Post by FiBsTeR on Dec 2^nd, 2007, 3:24pm

You might want to make sure that you 1) copied the problem right, 2) copied the answer to the problem correctly from the book, and 3) copied the answer from the correct problem.

pex's solution is the one for this particular problem:

2sqrt(-x+1) - sqrt(2x-5) = 0
2sqrt(-x+1) = sqrt(2x-5)
4(-x+1) = 2x-5
-4x + 4 = 2x-5
6x = 9
x = 3/2

Inserting the solution back to the problem tells us that this is a (and the only) solution.

Title: Re: Stuck on a radical
Post by TruthlessHero on Dec 2^nd, 2007, 4:56pm

Believe me, I've checked the question and answer at least a half dozen times, and I still see the problem, as stated, with a solution of -1/6. But, I hadn't really looked for a way to disprove it at the time of the posting ( I merely assumed the book was right. ). So I give a collective "thank you" to you three. I will be showing my professor the typo next class.

Title: Re: Stuck on a radical
Post by Sameer on Dec 2^nd, 2007, 7:12pm

I think if you have sqrt(2x+5) in there, the answer will be -1/6...

Title: Re: Stuck on a radical
Post by TruthlessHero on Dec 2^nd, 2007, 7:24pm

Yeah, I noticed that too, and my teacher agrees (emailed her) that that must be the typo.

Title: Re: Stuck on a radical
Post by Michael_Dagg on Dec 2^nd, 2007, 7:28pm

The problem solver made a mistake and solved this problem instead:

2 sqrt(-x + 1) - sqrt(2 x + 5)

whose solution is x = -1/6.

edit: as Sameer pointed out.

You'll discover that there are lots of errors in basic algebra
books like this one: over confidence on the part of the
problem solver and the fact that this level is generally
routine and boring leads to these sort of errors, and it is
not true that authors write all the problems or check
the solutions either. In fact, a publisher may at
the last minute hire a proofreader to read the book
when there simply isn't enough time to do it.