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November 20 2012, 06:57 AM  #1 
Commodore

A math puzzle
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November 20 2012, 07:04 AM  #2 
Admiral

Re: A math puzzle
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Don't be a douche. 
November 20 2012, 07:07 AM  #3 
Admiral
Location: I'm at WKRP

Re: A math puzzle
With the top being level 1, the transition from level 2 to level 3 is incorrect. that transition does not take into account 24 on the left and 40 on the right. ETA: Beaten to the answer while trying to come up with the right words.
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Baby, you and me were never meant to be, just maybe think of me once in a while... 
November 20 2012, 07:31 AM  #4 
Commodore
Location: milky way, outer spiral arm, Sol 3

Re: A math puzzle
924 = 15 2540 = 15 While techically (meaning the way the equation is being treated with completing the square, radicating [correct word??] etc.) the procedure is correct, you start the "proof" under the false premise that 15 = +15 This triggers a cascade of errors with the rest of the calculation, much like a dominoeffect: In Line #2 you get 1 = 31 In Lines #3 and #4 the equation reads as 1 = +1 The important thing  both in mathematics and in life  is to never take anything for granted but always to check the supposed facts yourself, without blindly relying on others.
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a hug a day keeps the psychiatrist away Last edited by rhubarbodendron; November 20 2012 at 07:44 AM. 
November 20 2012, 07:48 AM  #5  
World Famous Starship Captain

Re: A math puzzle
Given the leap of adding 16 to each side in statement 2, the transition from level 2 to level 3 is also correct. I think the main mistake is in the 4th statement  both sides should be divided by the same common multiplier to keep things equal, but instead the left is divided by (34) and the right by (54). Taking the rest of the sequence beyond that error, you still end up with a difference of 2 instead of equality, whether you physically subtract 4 from each side or just let them cancel each other out. Do correct me if I am wrong  I've just woken up.
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"In Germany, fear comes before sex... and if you're lucky, then a little bit later, an elf."  Victoria Coren Mitchell "Everybody has a secret world inside of them..."  Neil Gaiman
Last edited by Zulu Romeo; November 20 2012 at 08:12 AM. Reason: one more thing 

November 20 2012, 08:08 AM  #6 
Commodore
Location: milky way, outer spiral arm, Sol 3

Re: A math puzzle
At any rate you proved my point of never taking anything for granted and always checking the facts The trick with such equations is usually that you discreetly multiply with zero and then cancel down. In this case, however, it works differently: Line #1 reads as 15 = 15 which is correct Line #2 says 1 = 1 still correct Line #3 states 1² = +1² which is basically correct, as both is 1 but then at line #4 you radicate again which you shouldn't, because 1 is not +1. So line #4 is definitely wrong, and then the last line automatically gets wrong as well.
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a hug a day keeps the psychiatrist away 
November 20 2012, 10:54 AM  #7 
Admiral

Re: A math puzzle
__________________
Don't be a douche. 
November 20 2012, 01:16 PM  #8 
Vice Admiral

Re: A math puzzle
(a+b)²= a²+2ab+b² (ab)²=a²2ab+b² (ab)(a+b)=a²b²
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Not on strike. 
November 20 2012, 01:30 PM  #9 
Admiral

Re: A math puzzle
__________________
Don't be a douche. 
November 20 2012, 01:41 PM  #10 
Rear Admiral
Location: the real world

Re: A math puzzle
In line 3, when the expanded terms are reduced to a binomial, neither 35 nor 54 are binomials in the usual sense of unknown variables that cannot be summed because they are unknown. The usual procedure is to consolidate the constants, which would have given us 1 squared and 1 squared in line 4. Which are indeed equal. But then, it would have been much more obvious that square roots are commonly limited to the positive roots even though they are both positive and negative. For example, the square roots of 4 are 2 and 2, but only 2 is commonly written down. But here it is arbitrarily written, in effect, that one side the root is only 1 while on the other it is only +1. It should have been +1 and 1 on both sides. PS Another way of putting it: It is obvious that the square root of a^2 is both plus and minus a. But if we write (a)^2, the parentheses appear to exclude the negative root. The moral here is that parentheses are conveniences, not genuine mathematical operations.
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The people of this country need regime change here, not abroad. Last edited by stj; November 20 2012 at 02:21 PM. 
November 20 2012, 01:43 PM  #11 
Captain

Re: A math puzzle
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"They must be Borg, then... assimilate or die. Resistance is futile." 
November 20 2012, 01:48 PM  #12 
Commander
Location: Ood Sigma

Re: A math puzzle
The third line is correct: (34)^2 = (1)^2 = 1 (54)^2 = (1)^2 = 1 But it is dependent on the fact that 1 has square roots of both 1 and 1. 
November 20 2012, 04:13 PM  #13 
Rear Admiral
Location: On the beach

Re: A math puzzle
(34) = (54)(54)/(34) = 1x1/1 = 1 
November 20 2012, 05:48 PM  #14 
Commodore
Location: milky way, outer spiral arm, Sol 3

Re: A math puzzle
Totally offtopic, but I just have to ask: what kind of spider is the one in your avatar, Asbo Zaprudder? It's pretty!
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a hug a day keeps the psychiatrist away 
November 20 2012, 06:05 PM  #15 
Rear Admiral
Location: the real world

Re: A math puzzle
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The people of this country need regime change here, not abroad. 
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