wolfgang Posted January 9, 2012 Report Share Posted January 9, 2012 16 - 36 = 25 - 45 4^2 - (9x4) = 5^2 -(9x5) 4^2 - (9x4) + 81/4 = 5^2 -(9x5) + 81/4 ......by adding 81/4 to both sides (4-9/2)^2 = ( 5-9/2)^2......we can cancel the powers on both sides 4- 9/2 = 5- 9/2............add 9/2 to both sides to get: 4=5 !!! Am I wrong? Quote Link to comment Share on other sites More sharing options...
0 Peekay Posted January 9, 2012 Report Share Posted January 9, 2012 Reveal hidden contents You are wrong on the 5th step where you casually mention canceling the powers on both sides! (-1/2)^2 = (+1/2)^2 does not yield -1/2 = +1/2 But, definitely a good one! Quote Link to comment Share on other sites More sharing options...
0 Thalia Posted January 9, 2012 Report Share Posted January 9, 2012 (edited) Reveal hidden contents On 1/9/2012 at 9:55 PM, wolfgang said: 16 - 36 = 25 - 45 4^2 - (9x4) = 5^2 -(9x5) 4^2 - (9x4) + 81/4 = 5^2 -(9x5) + 81/4 ......by adding 81/4 to both sides (4-9/2)^2 = ( 5-9/2)^2......we can cancel the powers on both sides 4- 9/2 = 5- 9/2............add 9/2 to both sides to get: 4=5 !!! Am I wrong? What happened to the underlined parts in the next step? Edited January 9, 2012 by Thalia Quote Link to comment Share on other sites More sharing options...
0 Morningstar Posted January 10, 2012 Report Share Posted January 10, 2012 On 1/9/2012 at 10:17 PM, Peekay said: Reveal hidden contents You are wrong on the 5th step where you casually mention canceling the powers on both sides! (-1/2)^2 = (+1/2)^2 does not yield -1/2 = +1/2 But, definitely a good one! Reveal hidden contents Can't you do it by taking the square root of both sides, which is a "legal" mathematical operation?" Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 11, 2012 Report Share Posted January 11, 2012 On 1/9/2012 at 10:47 PM, Thalia said: Reveal hidden contents What happened to the underlined parts in the next step? This step is legitimate. Think about squaring the term (X-Y). This gives you X^2-2XY+Y^2. In this case X=4 and Y = 9/2 so the square of (4-9/2) = 4^2 -2x4x9/2+(81)/9=4^2-4x9+(81)/4 On 1/10/2012 at 12:21 AM, Morningstar said: Reveal hidden contents Can't you do it by taking the square root of both sides, which is a "legal" mathematical operation?" Reveal hidden contents When youy take the sqareroot, there are 2 possible roots since (-2)^2 and 2^2 both equal 4, when takeing the squareroot, we must consider which root is the appropriate. In this case note that the fith step which currently reads: 4- 9/2 = 5- 9/2 but by choosing the opposite sign on one side, we get instead 9/2-4=5-9/2 which indeed is a true statement since 1/2=1/2 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 11, 2012 Report Share Posted January 11, 2012 (edited) On 1/11/2012 at 1:28 PM, thoughtfulfellow said: This step is legitimate. Think about squaring the term (X-Y). This gives you X^2-2XY+Y^2. In this case X=4 and Y = 9/2 so the square of (4-9/2) = 4^2 -2x4x9/2+(81)/9=4^2-4x9+(81)/4 Reveal hidden contents When youy take the sqareroot, there are 2 possible roots since (-2)^2 and 2^2 both equal 4, when takeing the squareroot, we must consider which root is the appropriate. In this case note that the fith step which currently reads: 4- 9/2 = 5- 9/2 but by choosing the opposite sign on one side, we get instead 9/2-4=5-9/2 which indeed is a true statement since 1/2=1/2 Reveal hidden contents The next step would be to take the square root of both sides, but because of examples like the one Peekay gave, you must take the plus or minus square roots of both sides. As someone with some teaching experience in math, this is a common misake of only taking whats known as the "principle" square root (only the positive one) of both sides.<br /> The issue in this case is the the expression on the left (when you said cancel the powers on both sides) (4-9/2)^2 is negative (-0.5 in this case) where as the right (5-9/2)^2 is positive (0.5 in this case). EDIT: I didnt see the post that explained this already. Sorry for the second posting of the answer... Edited January 11, 2012 by jaustinsmith_2005 Quote Link to comment Share on other sites More sharing options...
0 Morningstar Posted January 11, 2012 Report Share Posted January 11, 2012 I see... My mistake. Good one! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 11, 2012 Report Share Posted January 11, 2012 (edited) This same question was found in Prof. Ramanujam's book and here goes the solution (4-9/2)^2 = (5-9/2)^2 => 4-9/2 = +/- (5-9/2) Since 4 is not equal to 5, hence, 4-9/2 = -(5-9/2) => 4-9/2 = -5 + 9/2 => 4+5 = 9/2 + 9/2 => 9 = 9 Left Hand Side = Right Hand Side Good luck with your maths exam I tried to use Spoiler, but it is not working in my machine for reasons i dont know. Hence posted the solution publicly. Edited January 11, 2012 by Satish.S Quote Link to comment Share on other sites More sharing options...
0 wolfgang Posted January 11, 2012 Author Report Share Posted January 11, 2012 I`d like to thank all of you.... The first mistake I did was at the 4th. step where I took only the positive squrt of 81/9 then was followed by other steps as mentioned by my friends above... thanks alot.... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 11, 2012 Report Share Posted January 11, 2012 here's a fun one. 0^0 = 1 therefore 0 = 1^(1/0) or 0 = log[0] 1 = log[10] 1 /log[10] 0 Quote Link to comment Share on other sites More sharing options...
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wolfgang
16 - 36 = 25 - 45
4^2 - (9x4) = 5^2 -(9x5)
4^2 - (9x4) + 81/4 = 5^2 -(9x5) + 81/4 ......by adding 81/4 to both sides
(4-9/2)^2 = ( 5-9/2)^2......we can cancel the powers on both sides
4- 9/2 = 5- 9/2............add 9/2 to both sides to get:
4=5 !!!
Am I wrong?
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