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 2007-06-18, 22:36 #1 davar55     May 2004 New York City 5×7×112 Posts Solve this equation Solve for x: (x+9)^(1/3) - (x-9)^(1/3) = 3 (This may be too easy for this forum, but I've always liked the solution method.)
 2007-06-18, 23:23 #2 ewmayer ∂2ω=0     Sep 2002 República de California 22×2,939 Posts x[sup]2[/sup]=80 Last fiddled with by ewmayer on 2007-06-18 at 23:23
2007-06-19, 07:50   #3
davieddy

"Lucan"
Dec 2006
England

11001010010102 Posts

Quote:
 Originally Posted by ewmayer x[sup]2[/sup]=80
Just as well this wasn't the homework help forum

2007-06-19, 12:20   #4
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

22·33·19 Posts
Solution!

Quote:
 Originally Posted by davar55 Solve for x: (x+9)^(1/3) - (x-9)^(1/3) = 3 (This may be too easy for this forum, but I've always liked the solution method.)

Lets have your method davar. Thank you!

Mally

 2007-06-19, 12:56 #5 Kees     Dec 2005 19610 Posts Taking cubes on both sides gives the result without any noteworthy manipulation. If there is an elegant solution or a smart substitution it still needs to be very short to beat the straightforward one
 2007-06-19, 14:23 #6 VolMike     Jun 2007 Moscow,Russia 7·19 Posts Equation doesn't have solution(s)
2007-06-19, 15:40   #7
davieddy

"Lucan"
Dec 2006
England

2×3×13×83 Posts

Quote:
 Originally Posted by Kees Taking cubes on both sides gives the result without any noteworthy manipulation.
The entertaining stage is:

-3[(x+9)1/3-(x-9)1/3](x2-81)1/3 = 9

at which point we use the original equation to substitute 3
for [...]

David

Last fiddled with by davieddy on 2007-06-19 at 15:42

2007-06-19, 15:51   #8
TimSorbet
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

11·389 Posts

Quote:
 Originally Posted by VolMike Equation doesn't have solution(s)
$x=sqrt{80}$

 2007-06-19, 21:14 #9 fetofs     Aug 2005 Brazil 2×181 Posts Not quite. $x = \pm\sqrt{80}$
2007-06-20, 07:32   #10
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

22·33·19 Posts
Solutions!

Quote:
 Originally Posted by davar55 Solve for x: (x+9)^(1/3) - (x-9)^(1/3) = 3 (This may be too easy for this forum, but I've always liked the solution method.)

A good problem but not instructional enough.

Its not good nor instructional getting straight solutions from the 'know all's'.

One right answer as ewmayer's is enough to tackle the problem

A hint from Keyes was good as it saved a lot of 'computation'. I have to use the term in these computer days as this is piffle for the comp.

As usual Davieddy's 'solution' and as he termed it 'entertainment' made things more confused and you can all see for your selves. Imagine substituting a whole equation for an integer ? And he claims to be a math's tutor !

A little knowledge is a very dangerous thing. Arrogance is even worse!

Now given that the solution is correct (I have not checked it out but accept Ewmayer's as correct) the next question is to generalise it from a particular problem.

My question is how would you solve the problem when the exponents are not equal? Lets say they are p and q and not just 1/3 ? How would you get the rationalising factor esp.
when there are three or more surds?

Thank you Davar55 as it made me revise my algebra!

BTW: if you have a better solution than keyes kindly respond and let me know.

Mally

Last fiddled with by mfgoode on 2007-06-20 at 07:35

2007-06-20, 08:03   #11
Chris Card

Aug 2004

7·19 Posts

Quote:
 Originally Posted by mfgoode As usual Davieddy's 'solution' and as he termed it 'entertainment' made things more confused and you can all see for your selves. Imagine substituting a whole equation for an integer ? And he claims to be a math's tutor !
What are you on about Mally? Davieddy's solution is exactly the way to do it. The substitution he suggests is valid, and the simplest way I can see to get to the solution.

Chris

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