0
$\begingroup$

I just saw this equation and I can't find out where's the problem:

$$25-45 = 16-36$$

$$25- 2 \cdot 5 \cdot \frac{9}{2} = 16- 2\cdot4\cdot\frac{9}{2}$$

$$25 - 2\cdot 5\cdot \frac{9}{2} + \frac{81}{4} = 16 - 2\cdot 4 \cdot \frac{9}{2} + \frac{81}{4}$$

$$\left( 5-\frac{9}{2} \right) ^2 = \left (4-\frac{9}{2} \right) ^2$$

$$5-\frac{9}{2} = 4 - \frac{9}{2}$$ $$5=4$$

  • 4
    you could try to solve the left and right side on each line and see where it starts to differ2012-07-14
  • 0
    Besides what has been said in the answers, there's actually another mistake: your brackets in the third line are not right.2012-07-14
  • 0
    The brackets were made wrong by an edit from Joe L. I have submitted a correction.2012-07-14
  • 0
    [Related, same fallacy.](http://math.stackexchange.com/questions/457490/22-5-error-in-proof)2016-11-19
  • 0
    Not the same, but rather similar approach: [$2+2 = 5$? error in proof](http://math.stackexchange.com/questions/457490/22-5-error-in-proof)2016-11-19

2 Answers 2

11

$a^2 = b^2$ does not imply that $a = b$.

  • 3
    It only implies $|a|=|b|$, i.e. $a=\pm b$.2012-07-14
8

$5-9/2$ is positive, $4-9/2$ is negative. They are not equal, although their squares are equal.